Non-Mixture Cure Model for Interval Censored Data: Simulation Study ABSTRACT

Size: px
Start display at page:

Download "Non-Mixture Cure Model for Interval Censored Data: Simulation Study ABSTRACT"

Transcription

1 Malaysan Journal of Mathematcal Scences 8(S): (2014) Specal Issue: Internatonal Conference on Mathematcal Scences and Statstcs 2013 (ICMSS2013) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Journal homepage: Non-Mxture Cure Model for Interval Censored Data: Smulaton Study Fauza Taweab, Noor Akma Ibrahm, Jayanth Arasan and Mohd Rzam Abu Bakar Insttute for Mathematcal Research, Unverst Putra Malaysa, UPM Serdang, Selangor, Malaysa E-mal: *Correspondng author ABSTRACT Wth the ongong advance n the medcal scences, we may qute often encounter data sets where some patents have been cured from dsease. Standard survval models are usually not approprate for modelng such data because they smply do not take nto account the possblty of cure. In ths artcle, a non-mxture cure model s proposed based on lognormal dstrbuton when the exact tme of the event of dsease s subject to nterval censorng. The maxmum lkelhood estmaton (MLE) method s mplemented to estmate the parameters and a smulaton study s conducted to assess the performance of the estmators under varous condtons. The study results demonstrate that the bas, standard error, and root mean squared error values of the parameters estmates decrease wth the ncrease n sample sze and that the estmaton method s more robust for data sets that have low censorng rates. Keywords: Non-mxture cure model, nterval censorng, maxmum lkelhood method, lognormal dstrbuton. 1. INTRODUCTION Due to advances n medcal scence, t s possble for a substantal proporton of patents not to experence the adverse event and these are thus consdered as cured subjects. Two of the major means of modelng such data are the mxture cure model and the non-mxture cure model. The mxture cure model was frst proposed by Boag (1949) to study cases where there a proporton of the patents recevng treatment for mouth cancer were cured. Ths model assumes that the entre populaton s composed of a mxture of

2 Fauza Taweab, Noor Akma Ibrahm, Jayanth Arasan & Mohd Rzam the cured and uncured ndvduals. The overall survval functon accordng to ths model can be expressed as S( t) p (1 p) S ( t) (1) where p s the probablty of cure and Su () t s the survval functon for the uncured patents. The mxture cure model has been nvestgated extensvely by many researchers ncludng Berkson et al. (1952), Kuk and Chen (1992), Peng and Dear (2000), Sposto (2002), and Km and Jhun (2008), Shuangge (2010), peng and u (2011), among others. Although ths model s common n survval data analyss, t mght not ft some types of data, especally n cancer studes snce t does not have the proportonal hazards structure when the probablty of cure s related to covarates and t does not closely descrbe the underlyng bologcal process. Chen et al. (1999) developed an alternatve useful model; the non-mxture cure model, for estmatng the cure rate. u 2. THE NON-MITURE CURE MODEL Ths model was developed by Chen et al (1999) based on the assumpton that the treatment leaves the patent wth a number of cancer cells, N, whch may grow slowly over tme and produce a detectable recurrence of cancer. The number of these cancer cells s assumed to follow a Posson dstrbuton wth a mean of θ. Suppose that the th clonogen needs tme, Z, to produce a cancer mass, then the recurrence of cancer can be defned by the random varable T such that T mn Z, 0 N, where Z are ndependent and dentcally dstrbuted wth F (.). Then, accordng to the Posson dstrbuton and the dstrbuton functon of the tme to detecton of cancer relapse, the survval functon for T s gven by S( t) P( no cancer by tme t) P( N 0) P( Z e N e 1 F N 0 N! F ( t) F ( t) p 1 t,..., Z ( t) N N t, N 1) (2) 38 Malaysan Journal of Mathematcal Scences

3 Non-Mxture Cure Model for Interval Censored Data: A Smulaton Study where p s the probablty of cure or the cure fracton whch can be defned as F( t) p S( ) lm e e (3) t Consderng that censorng tmes are ndependent and non-nformatve, Weston and Thompson (2010) showed that the lkelhood functon for the model based on rght censored data takes the form L n 1 log( p) f ( t ) S( t ) (4) where, 1 0 f event at t, f censored at t The model can be further extended by usng covarates to model the probablty of cure through θ. Moreover, a parametrc model can be specfed for the falure tme. In ths work, we consder that the mean of the cancer cells s related to covarates by e and that the lognormal dstrbuton for modelng the falure tme of the uncured subjects, 1 (ln t ) f ( t) exp[ 2 t 2 2 ln t F ( t) ( ), where s the standard normal dstrbuton functon. 2 ] 3. NON-MITURE CURE MODEL WITH INTERVAL CENSORED DATA Interval censorng occurs f nstead of observng the event tme T only an nterval [ L, R ] s observed where T [ L, R ], and L R. Here, L s the latest examnaton tme before the event and R s the earlest examnaton tme after the event. The subject s rght censored f she/he has been event- Malaysan Journal of Mathematcal Scences 39

4 Fauza Taweab, Noor Akma Ibrahm, Jayanth Arasan & Mohd Rzam free at the last known tme; T[ L, ). Based on these data, model (2) can be re-expressed as follows: P( L T R ) P( T L ) P( T R ) exp( e F( L )) exp( e F( R )) (5) In the cure model, there are two possbltes for the th rght subject ( R ); the subject s ether cured or she/he experences the event of nterest after the last examnaton tme (uncured). Further detals have been provded by Lu and Shen (2009). Then, P( L T ) exp( e F( L )) Now, we reformat the censorng ndcator as IR ( ) for T [ L, R ]. Then, the log-lkelhood functon for the n observed nterval data ( L, R,, ), 1,2,..., n, can be wrtten as: n L c exp( e F ( L )) exp( e F ( R )) exp( e F ( L )) 1 Ths can be smplfed to L c n 1 1 exp e ( F( R ) F( L )) exp( e F( L )) 1 (6) (7) Consderng lognormal dstrbuton, the log lkelhood functon of (7) s gven by: n l ln 1 exp e 1 ln L e ln R ln L (8) 40 Malaysan Journal of Mathematcal Scences

5 Non-Mxture Cure Model for Interval Censored Data: A Smulaton Study 4. SIMULATION STUDY AND RESULTS A smulaton study was conducted usng 1000 samples each wth sample szes of 100, 200, and 300 for the nterval-censored observatons and one covarate. The covarate values were generated from the Bernoull dstrbuton wth 0.5. For a gven, a random varable was smulated from the Bernoull dstrbuton wth exp[ exp( )]. If t s 1, then T and f t s 0, then we generate the falure tme values T from the lognormal dstrbuton. The true value of was chosen to be 0.01, correspondng to a cure rate of around Two dfferent values of the parameter were studed (0.7, 1) whle the value of 1 was chosen as the true value of the parameter. The vstng or examnaton tmes were smulated ndependent of and T followng Gouln (2008), wth dfferent percentages of nterval and rght censorng as well. It was assumed that the number of vstng tmes s 10 vsts for each subject and that the tme between two vsts has a unform dstrbuton on ( 0, c ), where c s a constant control censorng rate. In each smulaton, we assessed the bas, standard error (SE), and root mean square error (RMSE), bas SE, of the estmates and the results are collectvely presented n Table 1. In Table 1, we can see that the bases of estmates for are very small even for the hghest level of censorng and that these bases do not change much when the value of s changed from 0.7 to 1. On the other hand, the bas of the estmates for ncrease dramatcally n both levels of censorng when s ncreased to 1. For the estmates of, the bases are small when 0. 7 and the censorng rate s low. A comparson of the values of the SE provdes nformaton on whether the estmates of the proposed method are underestmated or overestmated. Good agreement n SE between the parameters was obtaned and the estmates for both the SE and RMSE decreased wth sample sze. Wth respect to the censorng rate, the performance of the suggested procedure s better under low levels of censorng than under heavy censorng. 2 2 Malaysan Journal of Mathematcal Scences 41

6 Fauza Taweab, Noor Akma Ibrahm, Jayanth Arasan & Mohd Rzam TABLE 1: Bas, SE, and RMSE of the estmates for two censorng rates (moderate (20-30 per cent) and heavy (40-60 per cent)) Censorng Rate Bas SE RMSE Bas SE RMSE n n n CONCLUSION In ths paper, the maxmum lkelhood estmates for the parameters of the lognormal non-mxture cure model n presence of nterval censored data were analyzed. It was found that the bas, SE, and RMSE of the estmates decrease when the sample sze ncreases. Also, t was shown that the estmaton method seems to provde consstent and better parameters estmates when the censorng rate s a bt low. 42 Malaysan Journal of Mathematcal Scences

7 Non-Mxture Cure Model for Interval Censored Data: A Smulaton Study ACKNOWLEDGEMENTS The authors gratefully acknowledged the fnancal support of Mnstry of Hgher Educaton Malaysa, and the nsttute for Mathematcal Research, Unverst Putra Malaysa for ther generous support of ths study. REFERENCES Berkson, J and Gage, R. P. (1952). Survval curve for cancer patents followng treatment. Journal of the Amercan Statstcal. 47: Boag, J.W. (1949). Maxmum lkelhood estmates of the proporton of patents cured by cancer therapy. Journal of the Royal Statstcal Socety. Seres B, 11: Chen, M. H, Ibrahm, J. G and Snha, D. (1999). A new Bayesan model for survval data wth a survvng fracton. Journal of the Amercan Statstcal Assocaton. 94 (447): Clare, L. Weston and John, R, Thompson. (2010). Modelng survval n chldhood cancer studes usng two- stage non-mxture cure models. Journal of Appled Statstcs. 37(9): Hao Lu and Shen Yu. (2009). A sem parametrc regresson cure model for nterval censored data. J Am Stat Assoc. 487: Km, Y. and Jhun, M. (2008). Cure rate model wth nterval censored data. Statst Med. 27: Kuk, A.Y.C and Chen, C.H.P. (1992). A mxture Modelng Combnng Logstc Regresson wth Proportonal Hazard Regresson. Bometrka.79: Peng, Y. and Dear, K.B.G. (2000). A nonparametrc mxture model for cure rate estmaton. Bometrcs. 56: Sposto, R. (2002). Cure model analyss n cancer: An applcaton to data from the chldren s cancer group. Statst. Med. 21: Malaysan Journal of Mathematcal Scences 43

8 Fauza Taweab, Noor Akma Ibrahm, Jayanth Arasan & Mohd Rzam Shuangge, Ma. (2010). Mxed case nterval censored data wth a cured subgroup. Statstca Snca. 20: Yngwe Peng and Janfeng u. (2011). An extended cure model and model selecton. Lfetme Data Anal. DOI /s Zhao, Guoln, M. A. (2008). Nonparametrc and parametrc survval analyss of censored data wth possble volaton of method assumptons. PhD thess, North Carolna Unversty. 44 Malaysan Journal of Mathematcal Scences

Computation of Higher Order Moments from Two Multinomial Overdispersion Likelihood Models

Computation of Higher Order Moments from Two Multinomial Overdispersion Likelihood Models Computaton of Hgher Order Moments from Two Multnomal Overdsperson Lkelhood Models BY J. T. NEWCOMER, N. K. NEERCHAL Department of Mathematcs and Statstcs, Unversty of Maryland, Baltmore County, Baltmore,

More information

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010 Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton

More information

Statistical inference for generalized Pareto distribution based on progressive Type-II censored data with random removals

Statistical inference for generalized Pareto distribution based on progressive Type-II censored data with random removals Internatonal Journal of Scentfc World, 2 1) 2014) 1-9 c Scence Publshng Corporaton www.scencepubco.com/ndex.php/ijsw do: 10.14419/jsw.v21.1780 Research Paper Statstcal nference for generalzed Pareto dstrbuton

More information

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth

More information

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications Durban Watson for Testng the Lack-of-Ft of Polynomal Regresson Models wthout Replcatons Ruba A. Alyaf, Maha A. Omar, Abdullah A. Al-Shha ralyaf@ksu.edu.sa, maomar@ksu.edu.sa, aalshha@ksu.edu.sa Department

More information

Influence Diagnostics on Competing Risks Using Cox s Model with Censored Data. Jalan Gombak, 53100, Kuala Lumpur, Malaysia.

Influence Diagnostics on Competing Risks Using Cox s Model with Censored Data. Jalan Gombak, 53100, Kuala Lumpur, Malaysia. Proceedngs of the 8th WSEAS Internatonal Conference on APPLIED MAHEMAICS, enerfe, Span, December 16-18, 5 (pp14-138) Influence Dagnostcs on Competng Rsks Usng Cox s Model wth Censored Data F. A. M. Elfak

More information

Chapter 20 Duration Analysis

Chapter 20 Duration Analysis Chapter 20 Duraton Analyss Duraton: tme elapsed untl a certan event occurs (weeks unemployed, months spent on welfare). Survval analyss: duraton of nterest s survval tme of a subject, begn n an ntal state

More information

4 Analysis of Variance (ANOVA) 5 ANOVA. 5.1 Introduction. 5.2 Fixed Effects ANOVA

4 Analysis of Variance (ANOVA) 5 ANOVA. 5.1 Introduction. 5.2 Fixed Effects ANOVA 4 Analyss of Varance (ANOVA) 5 ANOVA 51 Introducton ANOVA ANOVA s a way to estmate and test the means of multple populatons We wll start wth one-way ANOVA If the populatons ncluded n the study are selected

More information

DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION

DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION Internatonal Worshop ADVANCES IN STATISTICAL HYDROLOGY May 3-5, Taormna, Italy DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION by Sooyoung

More information

Andreas C. Drichoutis Agriculural University of Athens. Abstract

Andreas C. Drichoutis Agriculural University of Athens. Abstract Heteroskedastcty, the sngle crossng property and ordered response models Andreas C. Drchouts Agrculural Unversty of Athens Panagots Lazards Agrculural Unversty of Athens Rodolfo M. Nayga, Jr. Texas AMUnversty

More information

Regression Analysis of Clustered Failure Time Data under the Additive Hazards Model

Regression Analysis of Clustered Failure Time Data under the Additive Hazards Model A^VÇÚO 1 33 ò 1 5 Ï 217 c 1 Chnese Journal of Appled Probablty and Statstcs Oct., 217, Vol. 33, No. 5, pp. 517-528 do: 1.3969/j.ssn.11-4268.217.5.8 Regresson Analyss of Clustered Falure Tme Data under

More information

LINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables

LINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables LINEAR REGRESSION ANALYSIS MODULE VIII Lecture - 7 Indcator Varables Dr. Shalabh Department of Maematcs and Statstcs Indan Insttute of Technology Kanpur Indcator varables versus quanttatve explanatory

More information

Comparison of the Population Variance Estimators. of 2-Parameter Exponential Distribution Based on. Multiple Criteria Decision Making Method

Comparison of the Population Variance Estimators. of 2-Parameter Exponential Distribution Based on. Multiple Criteria Decision Making Method Appled Mathematcal Scences, Vol. 7, 0, no. 47, 07-0 HIARI Ltd, www.m-hkar.com Comparson of the Populaton Varance Estmators of -Parameter Exponental Dstrbuton Based on Multple Crtera Decson Makng Method

More information

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol Georgetown Unversty From the SelectedWorks of Mark J Meyer 8 Usng the estmated penetrances to determne the range of the underlyng genetc model n casecontrol desgn Mark J Meyer Neal Jeffres Gang Zheng Avalable

More information

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4) I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes

More information

Lecture 6: Introduction to Linear Regression

Lecture 6: Introduction to Linear Regression Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6

More information

Degradation Data Analysis Using Wiener Process and MCMC Approach

Degradation Data Analysis Using Wiener Process and MCMC Approach Engneerng Letters 5:3 EL_5_3_0 Degradaton Data Analyss Usng Wener Process and MCMC Approach Chunpng L Hubng Hao Abstract Tradtonal relablty assessment methods are based on lfetme data. However the lfetme

More information

Time to dementia onset: competing risk analysis with Laplace regression

Time to dementia onset: competing risk analysis with Laplace regression Tme to dementa onset: competng rsk analyss wth Laplace regresson Gola Santon, Debora Rzzuto, Laura Fratglon 4 th Nordc and Baltc STATA Users group meetng, Stockholm, November 20 Agng Research Center (ARC),

More information

International Journal of Industrial Engineering Computations

International Journal of Industrial Engineering Computations Internatonal Journal of Industral Engneerng Computatons 4 (03) 47 46 Contents lsts avalable at GrowngScence Internatonal Journal of Industral Engneerng Computatons homepage: www.growngscence.com/ec Modelng

More information

A Robust Method for Calculating the Correlation Coefficient

A Robust Method for Calculating the Correlation Coefficient A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal

More information

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.

More information

ANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)

ANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U) Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of

More information

GROUP SEQUENTIAL TEST OF NON-PARAMETRIC STATISTICS FOR SURVIVAL DATA

GROUP SEQUENTIAL TEST OF NON-PARAMETRIC STATISTICS FOR SURVIVAL DATA Hacettepe Journal of Mathematcs and Statstcs Volume 34 (2005), 67 74 GROUP SEQUETIAL TEST OF O-PARAMETRIC STATISTICS FOR SURVIVAL DATA Yaprak Parlak Demrhan and Sevl Bacanlı Receved 2 : 02 : 2005 : Accepted

More information

Comparison of Regression Lines

Comparison of Regression Lines STATGRAPHICS Rev. 9/13/2013 Comparson of Regresson Lnes Summary... 1 Data Input... 3 Analyss Summary... 4 Plot of Ftted Model... 6 Condtonal Sums of Squares... 6 Analyss Optons... 7 Forecasts... 8 Confdence

More information

Estimation of the Mean of Truncated Exponential Distribution

Estimation of the Mean of Truncated Exponential Distribution Journal of Mathematcs and Statstcs 4 (4): 84-88, 008 ISSN 549-644 008 Scence Publcatons Estmaton of the Mean of Truncated Exponental Dstrbuton Fars Muslm Al-Athar Department of Mathematcs, Faculty of Scence,

More information

Computing MLE Bias Empirically

Computing MLE Bias Empirically Computng MLE Bas Emprcally Kar Wa Lm Australan atonal Unversty January 3, 27 Abstract Ths note studes the bas arses from the MLE estmate of the rate parameter and the mean parameter of an exponental dstrbuton.

More information

Chapter 13: Multiple Regression

Chapter 13: Multiple Regression Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to

More information

The Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction

The Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also

More information

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition)

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition) Count Data Models See Book Chapter 11 2 nd Edton (Chapter 10 1 st Edton) Count data consst of non-negatve nteger values Examples: number of drver route changes per week, the number of trp departure changes

More information

Using T.O.M to Estimate Parameter of distributions that have not Single Exponential Family

Using T.O.M to Estimate Parameter of distributions that have not Single Exponential Family IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran

More information

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours UNIVERSITY OF TORONTO Faculty of Arts and Scence December 005 Examnatons STA47HF/STA005HF Duraton - hours AIDS ALLOWED: (to be suppled by the student) Non-programmable calculator One handwrtten 8.5'' x

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed

More information

x = , so that calculated

x = , so that calculated Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to

More information

THE ROYAL STATISTICAL SOCIETY 2006 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE

THE ROYAL STATISTICAL SOCIETY 2006 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE THE ROYAL STATISTICAL SOCIETY 6 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER I STATISTICAL THEORY The Socety provdes these solutons to assst canddates preparng for the eamnatons n future years and for

More information

Chapter 9: Statistical Inference and the Relationship between Two Variables

Chapter 9: Statistical Inference and the Relationship between Two Variables Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,

More information

International Journal of Engineering Research and Modern Education (IJERME) Impact Factor: 7.018, ISSN (Online): (

International Journal of Engineering Research and Modern Education (IJERME) Impact Factor: 7.018, ISSN (Online): ( CONSTRUCTION AND SELECTION OF CHAIN SAMPLING PLAN WITH ZERO INFLATED POISSON DISTRIBUTION A. Palansamy* & M. Latha** * Research Scholar, Department of Statstcs, Government Arts College, Udumalpet, Tamlnadu

More information

2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification

2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton

More information

Stat 642, Lecture notes for 01/27/ d i = 1 t. n i t nj. n j

Stat 642, Lecture notes for 01/27/ d i = 1 t. n i t nj. n j Stat 642, Lecture notes for 01/27/05 18 Rate Standardzaton Contnued: Note that f T n t where T s the cumulatve follow-up tme and n s the number of subjects at rsk at the mdpont or nterval, and d s the

More information

8/25/17. Data Modeling. Data Modeling. Data Modeling. Patrice Koehl Department of Biological Sciences National University of Singapore

8/25/17. Data Modeling. Data Modeling. Data Modeling. Patrice Koehl Department of Biological Sciences National University of Singapore 8/5/17 Data Modelng Patrce Koehl Department of Bologcal Scences atonal Unversty of Sngapore http://www.cs.ucdavs.edu/~koehl/teachng/bl59 koehl@cs.ucdavs.edu Data Modelng Ø Data Modelng: least squares Ø

More information

STK4080/9080 Survival and event history analysis

STK4080/9080 Survival and event history analysis SK48/98 Survval and event hstory analyss Lecture 7: Regresson modellng Relatve rsk regresson Regresson models Assume that we have a sample of n ndvduals, and let N (t) count the observed occurrences of

More information

CS 2750 Machine Learning. Lecture 5. Density estimation. CS 2750 Machine Learning. Announcements

CS 2750 Machine Learning. Lecture 5. Density estimation. CS 2750 Machine Learning. Announcements CS 750 Machne Learnng Lecture 5 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 539 Sennott Square CS 750 Machne Learnng Announcements Homework Due on Wednesday before the class Reports: hand n before

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data

More information

Negative Binomial Regression

Negative Binomial Regression STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...

More information

ECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics

ECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics ECOOMICS 35*-A Md-Term Exam -- Fall Term 000 Page of 3 pages QUEE'S UIVERSITY AT KIGSTO Department of Economcs ECOOMICS 35* - Secton A Introductory Econometrcs Fall Term 000 MID-TERM EAM ASWERS MG Abbott

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VIII LECTURE - 34 ANALYSIS OF VARIANCE IN RANDOM-EFFECTS MODEL AND MIXED-EFFECTS EFFECTS MODEL Dr Shalabh Department of Mathematcs and Statstcs Indan

More information

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands Content. Inference on Regresson Parameters a. Fndng Mean, s.d and covarance amongst estmates.. Confdence Intervals and Workng Hotellng Bands 3. Cochran s Theorem 4. General Lnear Testng 5. Measures of

More information

Estimation of accelerated failure time models with random effects

Estimation of accelerated failure time models with random effects Retrospectve Theses and Dssertatons Iowa State Unversty Capstones, Theses and Dssertatons 6 Estmaton of accelerated falure tme models wth random effects Yaqn Wang Iowa State Unversty Follow ths and addtonal

More information

The Occurrence and Timing of Events: The Application of Event History Models in Accounting and Finance Research

The Occurrence and Timing of Events: The Application of Event History Models in Accounting and Finance Research The Occurrence and Tmng of Events: The Applcaton of Event Hstory Models n Accountng and Fnance Research Marc J. LeClere Assstant Professor Department of Accountng School of Busness Admnstraton Loyola Unversty

More information

Maximum Likelihood Estimation of Binary Dependent Variables Models: Probit and Logit. 1. General Formulation of Binary Dependent Variables Models

Maximum Likelihood Estimation of Binary Dependent Variables Models: Probit and Logit. 1. General Formulation of Binary Dependent Variables Models ECO 452 -- OE 4: Probt and Logt Models ECO 452 -- OE 4 Maxmum Lkelhood Estmaton of Bnary Dependent Varables Models: Probt and Logt hs note demonstrates how to formulate bnary dependent varables models

More information

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding Recall: man dea of lnear regresson Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 8 Lnear regresson can be used to study an

More information

Credit Card Pricing and Impact of Adverse Selection

Credit Card Pricing and Impact of Adverse Selection Credt Card Prcng and Impact of Adverse Selecton Bo Huang and Lyn C. Thomas Unversty of Southampton Contents Background Aucton model of credt card solctaton - Errors n probablty of beng Good - Errors n

More information

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 008 Recall: man dea of lnear regresson Lnear regresson can be used to study

More information

Double Acceptance Sampling Plan for Time Truncated Life Tests Based on Transmuted Generalized Inverse Weibull Distribution

Double Acceptance Sampling Plan for Time Truncated Life Tests Based on Transmuted Generalized Inverse Weibull Distribution J. Stat. Appl. Pro. 6, No. 1, 1-6 2017 1 Journal of Statstcs Applcatons & Probablty An Internatonal Journal http://dx.do.org/10.18576/jsap/060101 Double Acceptance Samplng Plan for Tme Truncated Lfe Tests

More information

Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore

Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore Sesson Outlne Introducton to classfcaton problems and dscrete choce models. Introducton to Logstcs Regresson. Logstc functon and Logt functon. Maxmum Lkelhood Estmator (MLE) for estmaton of LR parameters.

More information

Bayesian Cure Rate Frailty Models with Application to a Root Canal Therapy Study

Bayesian Cure Rate Frailty Models with Application to a Root Canal Therapy Study Bometrcs 61, 552 558 June 2005 DOI: 10.1111/j.1541-0420.2005.040336.x Bayesan Cure Rate Fralty Models wth Applcaton to a Root Canal Therapy Study Guosheng Yn Department of Bostatstcs and Appled Mathematcs,

More information

Population Design in Nonlinear Mixed Effects Multiple Response Models: extension of PFIM and evaluation by simulation with NONMEM and MONOLIX

Population Design in Nonlinear Mixed Effects Multiple Response Models: extension of PFIM and evaluation by simulation with NONMEM and MONOLIX Populaton Desgn n Nonlnear Mxed Effects Multple Response Models: extenson of PFIM and evaluaton by smulaton wth NONMEM and MONOLIX May 4th 007 Carolne Bazzol, Sylve Retout, France Mentré Inserm U738 Unversty

More information

Statistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation

Statistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 13 The Smple Lnear Regresson Model and Correlaton 1999 Prentce-Hall, Inc. Chap. 13-1 Chapter Topcs Types of Regresson Models Determnng the Smple Lnear

More information

RELIABILITY ASSESSMENT

RELIABILITY ASSESSMENT CHAPTER Rsk Analyss n Engneerng and Economcs RELIABILITY ASSESSMENT A. J. Clark School of Engneerng Department of Cvl and Envronmental Engneerng 4a CHAPMAN HALL/CRC Rsk Analyss for Engneerng Department

More information

Logistic regression models 1/12

Logistic regression models 1/12 Logstc regresson models 1/12 2/12 Example 1: dogs look lke ther owners? Some people beleve that dogs look lke ther owners. Is ths true? To test the above hypothess, The New York Tmes conducted a quz onlne.

More information

Statistics for Economics & Business

Statistics for Economics & Business Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable

More information

BIO Lab 2: TWO-LEVEL NORMAL MODELS with school children popularity data

BIO Lab 2: TWO-LEVEL NORMAL MODELS with school children popularity data Lab : TWO-LEVEL NORMAL MODELS wth school chldren popularty data Purpose: Introduce basc two-level models for normally dstrbuted responses usng STATA. In partcular, we dscuss Random ntercept models wthout

More information

Cure Rate Models. Dr.R. Elangovan 1 * and B. Jayakumar 2. ISSN (Print) : ISSN (Online) :

Cure Rate Models. Dr.R. Elangovan 1 * and B. Jayakumar 2. ISSN (Print) : ISSN (Online) : Asa Pacfc Journal of Research Vol: I. Issue XXXVIII, Aprl 206 ISSN (Prnt : 2320-5504 ISSN (Onlne : 2347-4793 Cure Rate Models Dr.R. Elangovan * and B. Jayakumar 2 Professor, Department of Statstcs, Annamala

More information

Composite Hypotheses testing

Composite Hypotheses testing Composte ypotheses testng In many hypothess testng problems there are many possble dstrbutons that can occur under each of the hypotheses. The output of the source s a set of parameters (ponts n a parameter

More information

Interval Estimation of Stress-Strength Reliability for a General Exponential Form Distribution with Different Unknown Parameters

Interval Estimation of Stress-Strength Reliability for a General Exponential Form Distribution with Different Unknown Parameters Internatonal Journal of Statstcs and Probablty; Vol. 6, No. 6; November 17 ISSN 197-73 E-ISSN 197-74 Publshed by Canadan Center of Scence and Educaton Interval Estmaton of Stress-Strength Relablty for

More information

A New Method for Estimating Overdispersion. David Fletcher and Peter Green Department of Mathematics and Statistics

A New Method for Estimating Overdispersion. David Fletcher and Peter Green Department of Mathematics and Statistics A New Method for Estmatng Overdsperson Davd Fletcher and Peter Green Department of Mathematcs and Statstcs Byron Morgan Insttute of Mathematcs, Statstcs and Actuaral Scence Unversty of Kent, England Overvew

More information

MATH 829: Introduction to Data Mining and Analysis The EM algorithm (part 2)

MATH 829: Introduction to Data Mining and Analysis The EM algorithm (part 2) 1/16 MATH 829: Introducton to Data Mnng and Analyss The EM algorthm (part 2) Domnque Gullot Departments of Mathematcal Scences Unversty of Delaware Aprl 20, 2016 Recall 2/16 We are gven ndependent observatons

More information

CS-433: Simulation and Modeling Modeling and Probability Review

CS-433: Simulation and Modeling Modeling and Probability Review CS-433: Smulaton and Modelng Modelng and Probablty Revew Exercse 1. (Probablty of Smple Events) Exercse 1.1 The owner of a camera shop receves a shpment of fve cameras from a camera manufacturer. Unknown

More information

Change Point Estimation for Pareto Type-II Model

Change Point Estimation for Pareto Type-II Model Journal of Modern Appled Statstcal Methods Volume 3 Issue Artcle 5--04 Change Pont Estmaton for Pareto Type-II Model Gyan Prakash S. N. Medcal College, Agra, U. P., Inda, ggyanj@yahoo.com Follow ths and

More information

A Note on Test of Homogeneity Against Umbrella Scale Alternative Based on U-Statistics

A Note on Test of Homogeneity Against Umbrella Scale Alternative Based on U-Statistics J Stat Appl Pro No 3 93- () 93 NSP Journal of Statstcs Applcatons & Probablty --- An Internatonal Journal @ NSP Natural Scences Publshng Cor A Note on Test of Homogenety Aganst Umbrella Scale Alternatve

More information

Statistical analysis using matlab. HY 439 Presented by: George Fortetsanakis

Statistical analysis using matlab. HY 439 Presented by: George Fortetsanakis Statstcal analyss usng matlab HY 439 Presented by: George Fortetsanaks Roadmap Probablty dstrbutons Statstcal estmaton Fttng data to probablty dstrbutons Contnuous dstrbutons Contnuous random varable X

More information

Modeling and Simulation NETW 707

Modeling and Simulation NETW 707 Modelng and Smulaton NETW 707 Lecture 5 Tests for Random Numbers Course Instructor: Dr.-Ing. Magge Mashaly magge.ezzat@guc.edu.eg C3.220 1 Propertes of Random Numbers Random Number Generators (RNGs) must

More information

Parameters Estimation of the Modified Weibull Distribution Based on Type I Censored Samples

Parameters Estimation of the Modified Weibull Distribution Based on Type I Censored Samples Appled Mathematcal Scences, Vol. 5, 011, no. 59, 899-917 Parameters Estmaton of the Modfed Webull Dstrbuton Based on Type I Censored Samples Soufane Gasm École Supereure des Scences et Technques de Tuns

More information

Maximizing Overlap of Large Primary Sampling Units in Repeated Sampling: A comparison of Ernst s Method with Ohlsson s Method

Maximizing Overlap of Large Primary Sampling Units in Repeated Sampling: A comparison of Ernst s Method with Ohlsson s Method Maxmzng Overlap of Large Prmary Samplng Unts n Repeated Samplng: A comparson of Ernst s Method wth Ohlsson s Method Red Rottach and Padrac Murphy 1 U.S. Census Bureau 4600 Slver Hll Road, Washngton DC

More information

/ n ) are compared. The logic is: if the two

/ n ) are compared. The logic is: if the two STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence

More information

Using Multivariate Rank Sum Tests to Evaluate Effectiveness of Computer Applications in Teaching Business Statistics

Using Multivariate Rank Sum Tests to Evaluate Effectiveness of Computer Applications in Teaching Business Statistics Usng Multvarate Rank Sum Tests to Evaluate Effectveness of Computer Applcatons n Teachng Busness Statstcs by Yeong-Tzay Su, Professor Department of Mathematcs Kaohsung Normal Unversty Kaohsung, TAIWAN

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experments- MODULE LECTURE - 6 EXPERMENTAL DESGN MODELS Dr. Shalabh Department of Mathematcs and Statstcs ndan nsttute of Technology Kanpur Two-way classfcaton wth nteractons

More information

Semiparametric Methods of Time Scale Selection

Semiparametric Methods of Time Scale Selection 1 Semparametrc Methods of Tme Scale Selecton Therry Duchesne Unversty of Toronto, Toronto, Canada Abstract: In several relablty applcatons, there may not be a unque plausble scale n whch to analyze falure

More information

Effective plots to assess bias and precision in method comparison studies

Effective plots to assess bias and precision in method comparison studies Effectve plots to assess bas and precson n method comparson studes Bern, November, 016 Patrck Taffé, PhD Insttute of Socal and Preventve Medcne () Unversty of Lausanne, Swtzerland Patrck.Taffe@chuv.ch

More information

Jon Deeks and Julian Higgins. on Behalf of the Statistical Methods Group of The Cochrane Collaboration. April 2005

Jon Deeks and Julian Higgins. on Behalf of the Statistical Methods Group of The Cochrane Collaboration. April 2005 Standard statstcal algorthms n Cochrane revews Verson 5 Jon Deeks and Julan Hggns on Behalf of the Statstcal Methods Group of The Cochrane Collaboraton Aprl 005 Data structure Consder a meta-analyss of

More information

A note on regression estimation with unknown population size

A note on regression estimation with unknown population size Statstcs Publcatons Statstcs 6-016 A note on regresson estmaton wth unknown populaton sze Mchael A. Hdroglou Statstcs Canada Jae Kwang Km Iowa State Unversty jkm@astate.edu Chrstan Olver Nambeu Statstcs

More information

A joint frailty-copula model between disease progression and death for meta-analysis

A joint frailty-copula model between disease progression and death for meta-analysis CSA-KSS-JSS Specal Invted Sessons 4 / / 6 A jont fralty-copula model between dsease progresson and death for meta-analyss 3/5/7 Takesh Emura Graduate Insttute of Statstcs Natonal Central Unversty TAIWAN

More information

Limited Dependent Variables and Panel Data. Tibor Hanappi

Limited Dependent Variables and Panel Data. Tibor Hanappi Lmted Dependent Varables and Panel Data Tbor Hanapp 30.06.2010 Lmted Dependent Varables Dscrete: Varables that can take onl a countable number of values Censored/Truncated: Data ponts n some specfc range

More information

An (almost) unbiased estimator for the S-Gini index

An (almost) unbiased estimator for the S-Gini index An (almost unbased estmator for the S-Gn ndex Thomas Demuynck February 25, 2009 Abstract Ths note provdes an unbased estmator for the absolute S-Gn and an almost unbased estmator for the relatve S-Gn for

More information

On Outlier Robust Small Area Mean Estimate Based on Prediction of Empirical Distribution Function

On Outlier Robust Small Area Mean Estimate Based on Prediction of Empirical Distribution Function On Outler Robust Small Area Mean Estmate Based on Predcton of Emprcal Dstrbuton Functon Payam Mokhtaran Natonal Insttute of Appled Statstcs Research Australa Unversty of Wollongong Small Area Estmaton

More information

Bias-correction under a semi-parametric model for small area estimation

Bias-correction under a semi-parametric model for small area estimation Bas-correcton under a sem-parametrc model for small area estmaton Laura Dumtrescu, Vctora Unversty of Wellngton jont work wth J. N. K. Rao, Carleton Unversty ICORS 2017 Workshop on Robust Inference for

More information

STAT 3008 Applied Regression Analysis

STAT 3008 Applied Regression Analysis STAT 3008 Appled Regresson Analyss Tutoral : Smple Lnear Regresson LAI Chun He Department of Statstcs, The Chnese Unversty of Hong Kong 1 Model Assumpton To quantfy the relatonshp between two factors,

More information

Testing for seasonal unit roots in heterogeneous panels

Testing for seasonal unit roots in heterogeneous panels Testng for seasonal unt roots n heterogeneous panels Jesus Otero * Facultad de Economía Unversdad del Rosaro, Colomba Jeremy Smth Department of Economcs Unversty of arwck Monca Gulett Aston Busness School

More information

On an Extension of Stochastic Approximation EM Algorithm for Incomplete Data Problems. Vahid Tadayon 1

On an Extension of Stochastic Approximation EM Algorithm for Incomplete Data Problems. Vahid Tadayon 1 On an Extenson of Stochastc Approxmaton EM Algorthm for Incomplete Data Problems Vahd Tadayon Abstract: The Stochastc Approxmaton EM (SAEM algorthm, a varant stochastc approxmaton of EM, s a versatle tool

More information

Hydrological statistics. Hydrological statistics and extremes

Hydrological statistics. Hydrological statistics and extremes 5--0 Stochastc Hydrology Hydrologcal statstcs and extremes Marc F.P. Berkens Professor of Hydrology Faculty of Geoscences Hydrologcal statstcs Mostly concernes wth the statstcal analyss of hydrologcal

More information

How its computed. y outcome data λ parameters hyperparameters. where P denotes the Laplace approximation. k i k k. Andrew B Lawson 2013

How its computed. y outcome data λ parameters hyperparameters. where P denotes the Laplace approximation. k i k k. Andrew B Lawson 2013 Andrew Lawson MUSC INLA INLA s a relatvely new tool that can be used to approxmate posteror dstrbutons n Bayesan models INLA stands for ntegrated Nested Laplace Approxmaton The approxmaton has been known

More information

Spatial Modelling of Peak Frequencies of Brain Signals

Spatial Modelling of Peak Frequencies of Brain Signals Malaysan Journal of Mathematcal Scences 3(1): 13-6 (9) Spatal Modellng of Peak Frequences of Bran Sgnals 1 Mahendran Shtan, Hernando Ombao, 1 Kok We Lng 1 Department of Mathematcs, Faculty of Scence, and

More information

Statistics for Business and Economics

Statistics for Business and Economics Statstcs for Busness and Economcs Chapter 11 Smple Regresson Copyrght 010 Pearson Educaton, Inc. Publshng as Prentce Hall Ch. 11-1 11.1 Overvew of Lnear Models n An equaton can be ft to show the best lnear

More information

QUASI-LIKELIHOOD APPROACH TO RATER AGREEMENT PLUS LINEAR BY LINEAR ASSOCIATION MODEL FOR ORDINAL CONTINGENCY TABLES

QUASI-LIKELIHOOD APPROACH TO RATER AGREEMENT PLUS LINEAR BY LINEAR ASSOCIATION MODEL FOR ORDINAL CONTINGENCY TABLES Journal of Statstcs: Advances n Theory and Applcatons Volume 6, Number, 26, Pages -5 Avalable at http://scentfcadvances.co.n DOI: http://dx.do.org/.8642/jsata_72683 QUASI-LIKELIHOOD APPROACH TO RATER AGREEMENT

More information

Efficient nonresponse weighting adjustment using estimated response probability

Efficient nonresponse weighting adjustment using estimated response probability Effcent nonresponse weghtng adjustment usng estmated response probablty Jae Kwang Km Department of Appled Statstcs, Yonse Unversty, Seoul, 120-749, KOREA Key Words: Regresson estmator, Propensty score,

More information

Homework Assignment 3 Due in class, Thursday October 15

Homework Assignment 3 Due in class, Thursday October 15 Homework Assgnment 3 Due n class, Thursday October 15 SDS 383C Statstcal Modelng I 1 Rdge regresson and Lasso 1. Get the Prostrate cancer data from http://statweb.stanford.edu/~tbs/elemstatlearn/ datasets/prostate.data.

More information

Applications of GEE Methodology Using the SAS System

Applications of GEE Methodology Using the SAS System Applcatons of GEE Methodology Usng the SAS System Gordon Johnston Maura Stokes SAS Insttute Inc, Cary, NC Abstract The analyss of correlated data arsng from repeated measurements when the measurements

More information

DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR. Introductory Econometrics 1 hour 30 minutes

DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR. Introductory Econometrics 1 hour 30 minutes 25/6 Canddates Only January Examnatons 26 Student Number: Desk Number:...... DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR Department Module Code Module Ttle Exam Duraton

More information

Parametric fractional imputation for missing data analysis

Parametric fractional imputation for missing data analysis Secton on Survey Research Methods JSM 2008 Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Wayne Fuller Abstract Under a parametrc model for mssng data, the EM algorthm s a popular tool

More information

Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution

Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution JIRSS 013 Vol. 1, No., pp 35-5 Downloaded from jrss.rstat.r at 1:45 +0430 on Monday September 17th 018 Asymptotc ffcences of the ML Based on Bvarate Record Values from Bvarate Normal Dstrbuton Morteza

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for U Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for U Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Adjusted Control Lmts for U Charts Copyrght 207 by Taylor Enterprses, Inc., All Rghts Reserved. Adjusted Control Lmts for U Charts Dr. Wayne A. Taylor Abstract: U charts are used

More information