A Generalized Class of Estimators for Finite Population Variance in Presence of Measurement Errors
|
|
- Godfrey Casey
- 5 years ago
- Views:
Transcription
1 Joural of Moder Applied Statistical Methods Volume Issue Article A Geeralized Class of Estimators for Fiite Populatio Variace i Presece of Measuremet Errors Praas Sharma Baaras Hidu Uiversit, Varaasi, Idia, praassharma0@gmail.com Rajesh Sigh Baaras Hidu Uiversit, Varaasi, Idia, rsighstat@gmail.com Follow this ad additioal works at: Part of the Applied Statistics Commos, Social ad Behavioral Scieces Commos, ad the Statistical Theor Commos Recommeded Citatio Sharma, Praas ad Sigh, Rajesh (03) "A Geeralized Class of Estimators for Fiite Populatio Variace i Presece of Measuremet Errors," Joural of Moder Applied Statistical Methods: Vol. : Iss., Article 3. DOI: 0.37/jmasm/ Available at: This Regular Article is brought to ou for free ad ope access b the Ope Access Jourals at DigitalCommos@WaeState. It has bee accepted for iclusio i Joural of Moder Applied Statistical Methods b a authorized editor of DigitalCommos@WaeState.
2 Joural of Moder Applied Statistical Methods November 03, Vol., No., 3-. Copright 03 JMASM, Ic. ISSN A Geeralized Class of Estimators for Fiite Populatio Variace i Presece of Measuremet Errors Praas Sharma Baaras Hidu Uiversit Varaasi, Idia Rajesh Sigh Baaras Hidu Uiversit Varaasi, Idia The problem of estimatig the populatio variace is preseted usig auiliar iformatio i the presece of measuremet errors. The estimators i this article use auiliar iformatio to improve efficiec ad assume that measuremet error is preset both i stud ad auiliar variable. A umerical stud is carried out to compare the performace of the proposed estimator with other estimators ad the variace per uit estimator i the presece of measuremet errors. Kewords: Populatio mea, stud variate, auiliar variates, mea squared error, measuremet errors, efficiec. Itroductio Over the past several decades, statisticias are paig their attetio towards the problem of estimatio of parameters i the presece of measuremet errors. I surve samplig, the properties of estimators based o data usuall presuppose that the observatios are the correct measuremets o characteristics beig studied. However, this assumptio is ot satisfied i ma applicatios ad data is cotamiated with measuremet errors, such as o-respose errors, reportig errors, ad computig errors. These measuremet errors make the result ivalid, which are meat for o measuremet error case. If measuremet errors are ver small ad we ca eglect it, the the statistical ifereces based o observed data cotiue to remai valid. O the cotrar, whe the are ot appreciabl small ad egligible, the ifereces ma ot be simpl ivalid ad iaccurate but ma ofte lead to uepected, udesirable ad ufortuate cosequeces (see Srivastava ad Shalabh, 00). Some importat sources of measuremet errors i Praas Sharma is a Research Fellow i the Departmet of Statistics. him at praassharma0@gmail.com. Rajesh Sigh is Assistat professor i the Departmet of Statistics. at: rsighstat@gmail.com. 3
3 A CLASS OF ESTIMATORS FOR FINITE POPULATION VARIANCE surve data are discussed i Cochra (968), Shalabh (997), ad Sud ad Srivastva (000). Sigh ad Karpe (008, 00), Kumar et al. (0a, b) studied some estimators of populatio mea uder measuremet error. Ma authors, icludig Das ad Tripathi (978), Srivastava ad Jhajj (980), Sigh ad Karpe (009) ad Diaa ad Giorda (0), studied the estimatio of populatio Variace of the stud variable usig auiliar iformatio i the presece of measuremet errors. The problem of estimatig the populatio variace ad its properties are studied here i the presece of measuremet errors. Cosider a fiite populatio U (U, U,... U N) of N uits. Let Y ad X be the stud variate ad auiliar variate, respectivel. Suppose a set of paired observatios are obtaied through simple radom samplig procedure o two characteristics X ad Y. Further assume that i ad i for the i th samplig uits are observed with measuremet error as opposed to their true values (X i, Y i ) For a simple radom samplig scheme, let ( i, i ) be observed values istead of the true values (X i, Y i ) for i th (i..) uit, as ui i Yi () v X () i i i where u i ad v i are associated measuremet errors which are stochastic i ature with mea zero ad variaces u ad v, respectivel. Further, let the u i s ad v i s are ucorrelated although X i s ad Y i s are correlated. Let the populatio meas of X ad Y characteristics be µ ad µ, populatio variaces of (, ) be (, ) ad let ρ be the populatio correlatio coefficiet betwee ad respectivel (see Maisha ad Sigh (00)). Notatios Let i, i, be the ubiased estimator of populatio meas X i i ad Y, respectivel but s ( ) i ad s ( ) i are ot i i ubiased estimator of (, ), respectivel. The epected values of s ad s i the presece of measuremet error are, give b, 3
4 SHARMA & SINGH ( ) E s + v ( ) E s + u Whe the error variace v is kow, the ubiased estimator of, is ˆ s v > 0, ad whe u is kow, the the ubiased estimator of is ˆ s u 0 Defie >. ( 0 ) ( e ) ˆ + e µ + such that E( e 0 ) ( ) E e 0, Ee ( ) C v + C θ, ad to the first degree of approimatio (whe fiite populatio correctio factor is igored) A 0, ( ) E e where, E( ee) 0 λc. A θ u u γ + γu u µ ( ) ( ) EY i µ µ (, ) λ, C, µ, θ + v, γ ( ) 3 β, ( ) 3 µ ( u) µ ( ) γu β u, β ( u), β ( ), µ ( u) µ ( ), ( ) ( ) u Eu i µ., 33
5 A CLASS OF ESTIMATORS FOR FINITE POPULATION VARIANCE θ ad θ are the reliabilit ratios of X ad Y, respectivel, lig betwee 0 ad. Estimator of populatio variace uder measuremet error Accordig to Koucu ad Kadilar (00), a regressio tpe estimator t is defied as t w ˆ + w ( µ ) (3) where w ad w are costats that have o restrictio. Epressio (3) ca be writte as t ( w ) + w e w µ e () 0 Takig epectatio both sides of (), results i Bias( t ) ( w ) (5) Squarig both sides of () ( ) ( ) t w + w e0 wµ e (6) or ( ) t ( w ) + w e + w µ e + ( w ) w e 0 0 ( w ) w µ e ww µ e0e) (7) Simplifig equatio (7), takig epectatios ad usig otatios, results i the mea square error of t up to first order of approimatio, as A C ww µ λc MSE( t) w( + ) + ( w) + w µ θ (8) 3
6 SHARMA & SINGH I the case, whe the measuremet error is zero, MSE of t without measuremet error is give b, * C C MSE ( t) { γ + + } + ( w) + w µ ww µ λ (9) ad M u u u C v t γ u + w + + µ (0) is the cotributio of measuremet errors i the MSE of estimator t. Differetiatig (8) with respect to w ad w partiall, equatig them to zero ad after simplificatio, results i the optimum values of w ad w, respectivel as w B C * *, w C AB C AB () A µ C µ Cλ where, A ( + ), B ad C. θ * * Usig the values of ω ad ω from equatio () ito equatio (8), gives the miimum MSE of the estimator t i terms of A, B ad C as ( C AB) MSE( t) mi 3BC AB BC + () ( C AB) Aother estimator uder measuremet error Based o Solaki ad Sigh (0), a estimator t 3 is defied as 35
7 A CLASS OF ESTIMATORS FOR FINITE POPULATION VARIANCE t ( ) ( + ) α β µ ˆ - ep µ µ (3) where α ad β are suitabl chose costats. Epressig the estimator t, i terms of e s is t ˆ ( e) α ep ( βe ) e + + () Epadig equatio () ad simplifig results i k e ( t ) e0 ( e+ ee 0 ) ( k k) 8 (5) where k ( β α) +. O takig epectatios of both sides of (5), the bias of the estimator t 3 up to the first order of approimatio is obtaied as Bias t ( ) λc k - 8 k k C θ (6) Squarig both sides of (5) ad after simplificatio, k t e0 + e ke0e ( ) (7) Takig epectatios of (7) ad usig otatios, the MSE of estimator t is calculated as MSE( t) A + C k C θ k θ λ θ (8) 36
8 SHARMA & SINGH Differetiatig equatio (8) with respect to k ad equatig to zero ad after simplificatio the optimum value of k is k * λθ (9) C Puttig the optimum value of k from (9) to (8), results i the miimum MSE of estimator t as MSE( t) mi A λθ (0) Remark: Sigh ad Karpe (009) defied a class of estimator for as t d ˆ db ( ) () where, d(b) is a fuctio of b such that d(), ad certai other coditios, similar to those give i Srivastava (97). The miimum MSE of t d is give b, MSE( t ) mi d A λθ () which is the same as the miimum MSE of estimator t, give i equatio (0). A Geeral Class of Estimators A geeral class of estimator t 3 is proposed as ( ) ( ) α β µ t ˆ 3 m + m( µ ) - ep µ + µ (3) Where m ad m are costats chose so as to miimize the mea squared error of the estimator t 3. Equatio (3) ca be epressed i terms of e s as 37
9 A CLASS OF ESTIMATORS FOR FINITE POPULATION VARIANCE ( k k) k t3 m + m e0 mµ e e e 8 () Epadig equatio () ad subtractig from both sides, results i k t m m e + m e m µ e ( ) ( ) 3 0 e mk k m( k k) ee 0 + mµ e 8 (5) O takig epectatios of both sides of (5) the bias of the estimator t 3 up to the first order approimatio is obtaied as mk Bias t m m k k + m (6) C λc k C 3 µ 8 θ θ ( ) ( ) ( ) Squarig both sides of (5), results i k t3 m m e+ m e0 mµ e ( ) ( ) (7) Simplifig equatio (7) ad takig epectatios both sides the MSE of estimator t 3 up to the first order of approimatio is obtaied as ( ) MSE( t3) m + mp + mq mm R (8) where A kc k P C θ λ + +, µ C Q ad θ C R k + λc θ µ. Miimizig MSE t 3 with respect to m ad m the optimum values of m ad m is 38
10 SHARMA & SINGH Q * R * m ad m R PQ R PQ Puttig the optimum values of m ad m i equatio (8) results i the miimum MSE of estimator t 3 as MSE t 3 ( ) Q ( PQ R ) (9) Empirical Stud Data Statistics: The data used for empirical stud was take from Gujrati ad Sageetha (007) - pg, 539., where, Y i True cosumptio epediture, X i True icome, i Measured cosumptio epediture, Measured icome. i From the data give we get the followig parameter values: Table. Parameter values from empirical data N µ µ ρ u v Table. Showig the MSE of the estimators with ad without measuremet errors Estimators MSE without meas. Error Cotributio of meas. Errors i MSE MSE with meas. Errors ˆ t
11 A CLASS OF ESTIMATORS FOR FINITE POPULATION VARIANCE Table cotiued. Estimators MSE without meas. Error Cotributio of meas. Errors i MSE MSE with meas. Errors t mi t ( α, β 0) mi ( α 0, β ) ( α, β ) ( α, β ) ( α 0, β ) ( α 0.9, β ) Coclusio Table shows that the MSE of proposed estimator t 3 (for α 0.9, β ) is miimum amog all other estimators cosidered. It is also observed that the effect due to measuremet error o the estimator t ad usual estimators is less tha the effect o the estimator t uder measuremet error for this give data set. Refereces Alle, J., Sigh, H. P., & Smaradache, F. (003). A famil of estimators Of populatio mea usig multi auiliar iformatio i presece of measuremet errors. Iteratioal Joural of Social Ecoomics 30(7), Cochra, W. G. (968). Errors of Measuremet i statistics. Techometrics 0, Das, A. K., & Tripathi, T. P. (978). Use of auiliar iformatio i estimatig the Fiite populatio variace. Sakha C, 39-8 Diaa, G., & Giorda, M. (0). Fiite Populatio Variace Estimatio i Presece of Measuremet Errors. Commuicatio i Statistics Theor ad Methods,, Gujarati, D. N., & Sageetha (007). Basic ecoometrics. McGraw Hill. Koucu, N., & Kadilar, C. (00). O the famil of estimators of Populatio mea i stratified samplig.pakista Joural of Statistics, 6,
12 SHARMA & SINGH Kumar, M., Sigh, R., Sigh, A. K., & Smaradache, F. (0a). Some ratio Tpe estimators uder measuremet errors. World Applied Scieces Joural, (), Kumar, M., Sigh, R., Sawa, N., & Chauha, P. (0b). Epoetial ratio method Of estimators i the presece of measuremet errors. Iteratioal Joural of Agricultural ad Statistical Scieces 7(), Maisha, M., & Sigh, R. K. (00). Role of regressio estimator ivolvig Measuremet errors. Brazilia Joural of Probabilit ad Statistics 6, Shalabh. (997). Ratio method of estimatio i the presece of measuremet errors. Joural of Idia Societ of Agricultural Statistics 50(), Sigh, H. P. & Karpe, N. (008). Ratio product estimator for populatio mea i presece of measuremet errors. Joural of Applied Statistical Scieces, 6(), 9-6. Sigh, H. P. & Karpe, N. (009). Class of estimators usig auiliar Iformatio for estimatig fiite populatio variace i presece of measuremet errors. Commuicatio i Statistics Theor ad Methods, 38, Sigh, H. P. & Karpe, N. (00). Effect of measuremet errors o the Separate Ad combied ratio ad product estimators i Stratified radom samplig. Joural of Moder Applied Statistical Methods, 9(), Solaki R., Sigh H.P., & Rathour A. (0). A alterative estimator for estimatig the fiite populatio mea usig auiliar iformatio i sample surves. ISRN Probabilit ad Statistics, doi:0.50/0/ Srivastava, M. S. (97). O Fied-Width Cofidece Bouds for Regressio Parameters, Aals of Mathematical Statistics,, 03-. Srivastava, A., K., & Shalabh. (00). Effect of Measuremet Errors O the Regressio Method of Estimatio i Surve Samplig. Joural of Statistical Research, 35(), 35-. Srivastava, S. K., & Jhajj, H.S. (980) A class of estimators usig auiliar iformatio for estimatig fiite populatio variace. Sakha Ser. C, Sud, U. C., & Srivastava, S. K. (000). Estimatio of populatio mea i repeat surves i the presece of measuremet errors. Joural of the Idia Societ of Agricultural Statistics, 53(), 5-33.
Method of Estimation in the Presence of Nonresponse and Measurement Errors Simultaneously
Joural of Moder Applied Statistical Methods Volume 4 Issue Article 5--05 Method of Estimatio i the Presece of Norespose ad Measuremet Errors Simultaeousl Rajesh Sigh Sigh Baaras Hidu Uiversit, Varaasi,
More informationImproved exponential estimator for population variance using two auxiliary variables
OCTOGON MATHEMATICAL MAGAZINE Vol. 7, No., October 009, pp 667-67 ISSN -5657, ISBN 97-973-55-5-0, www.hetfalu.ro/octogo 667 Improved expoetial estimator for populatio variace usig two auxiliar variables
More informationA Family of Unbiased Estimators of Population Mean Using an Auxiliary Variable
Advaces i Computatioal Scieces ad Techolog ISSN 0973-6107 Volume 10, Number 1 (017 pp. 19-137 Research Idia Publicatios http://www.ripublicatio.com A Famil of Ubiased Estimators of Populatio Mea Usig a
More informationA General Family of Estimators for Estimating Population Variance Using Known Value of Some Population Parameter(s)
Rajesh Sigh, Pakaj Chauha, Nirmala Sawa School of Statistics, DAVV, Idore (M.P.), Idia Floreti Smaradache Uiversity of New Meico, USA A Geeral Family of Estimators for Estimatig Populatio Variace Usig
More informationSome Exponential Ratio-Product Type Estimators using information on Auxiliary Attributes under Second Order Approximation
; [Formerly kow as the Bulleti of Statistics & Ecoomics (ISSN 097-70)]; ISSN 0975-556X; Year: 0, Volume:, Issue Number: ; It. j. stat. eco.; opyright 0 by ESER Publicatios Some Expoetial Ratio-Product
More informationVaranasi , India. Corresponding author
A Geeral Family of Estimators for Estimatig Populatio Mea i Systematic Samplig Usig Auxiliary Iformatio i the Presece of Missig Observatios Maoj K. Chaudhary, Sachi Malik, Jayat Sigh ad Rajesh Sigh Departmet
More informationA Family of Efficient Estimator in Circular Systematic Sampling
olumbia Iteratioal Publishig Joural of dvaced omputig (0) Vol. o. pp. 6-68 doi:0.776/jac.0.00 Research rticle Famil of Efficiet Estimator i ircular Sstematic Samplig Hemat K. Verma ad Rajesh Sigh * Received
More informationUse of Auxiliary Information for Estimating Population Mean in Systematic Sampling under Non- Response
Maoj K. haudhar, Sachi Malik, Rajesh Sigh Departmet of Statistics, Baaras Hidu Uiversit Varaasi-005, Idia Floreti Smaradache Uiversit of New Mexico, Gallup, USA Use of Auxiliar Iformatio for Estimatig
More informationImproved Class of Ratio -Cum- Product Estimators of Finite Population Mean in two Phase Sampling
Global Joural of Sciece Frotier Research: F Mathematics ad Decisio Scieces Volume 4 Issue 2 Versio.0 Year 204 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic. (USA
More informationChain ratio-to-regression estimators in two-phase sampling in the presence of non-response
ProbStat Forum, Volume 08, July 015, Pages 95 10 ISS 0974-335 ProbStat Forum is a e-joural. For details please visit www.probstat.org.i Chai ratio-to-regressio estimators i two-phase samplig i the presece
More informationNew Ratio Estimators Using Correlation Coefficient
New atio Estimators Usig Correlatio Coefficiet Cem Kadilar ad Hula Cigi Hacettepe Uiversit, Departmet of tatistics, Betepe, 06800, Akara, Turke. e-mails : kadilar@hacettepe.edu.tr ; hcigi@hacettepe.edu.tr
More informationEstimation of the Population Mean in Presence of Non-Response
Commuicatios of the Korea Statistical Society 0, Vol. 8, No. 4, 537 548 DOI: 0.535/CKSS.0.8.4.537 Estimatio of the Populatio Mea i Presece of No-Respose Suil Kumar,a, Sadeep Bhougal b a Departmet of Statistics,
More informationEstimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation
Ope Joural o Statistics, 05, 5, -9 Published Olie Februar 05 i SciRes. http://www.scirp.org/joural/ojs http://dx.doi.org/0.436/ojs.05.500 Estimatio o Populatio Ratio i Post-Stratiied Samplig Usig Variable
More informationControl Charts for Mean for Non-Normally Correlated Data
Joural of Moder Applied Statistical Methods Volume 16 Issue 1 Article 5 5-1-017 Cotrol Charts for Mea for No-Normally Correlated Data J. R. Sigh Vikram Uiversity, Ujjai, Idia Ab Latif Dar School of Studies
More informationModified Ratio Estimators Using Known Median and Co-Efficent of Kurtosis
America Joural of Mathematics ad Statistics 01, (4): 95-100 DOI: 10.593/j.ajms.01004.05 Modified Ratio s Usig Kow Media ad Co-Efficet of Kurtosis J.Subramai *, G.Kumarapadiya Departmet of Statistics, Podicherry
More informationEstimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable
Iteratioal Joural of Probability ad Statistics 01, 1(4: 111-118 DOI: 10.593/j.ijps.010104.04 Estimatio of Populatio Mea Usig Co-Efficiet of Variatio ad Media of a Auxiliary Variable J. Subramai *, G. Kumarapadiya
More informationEnhancing ratio estimators for estimating population mean using maximum value of auxiliary variable
J.Nat.Sci.Foudatio Sri Laka 08 46 (: 45-46 DOI: http://d.doi.org/0.408/jsfsr.v46i.8498 RESEARCH ARTICLE Ehacig ratio estimators for estimatig populatio mea usig maimum value of auiliar variable Nasir Abbas,
More informationEstimation of Gumbel Parameters under Ranked Set Sampling
Joural of Moder Applied Statistical Methods Volume 13 Issue 2 Article 11-2014 Estimatio of Gumbel Parameters uder Raked Set Samplig Omar M. Yousef Al Balqa' Applied Uiversity, Zarqa, Jorda, abuyaza_o@yahoo.com
More informationJournal of Scientific Research Vol. 62, 2018 : Banaras Hindu University, Varanasi ISSN :
Joural of Scietific Research Vol. 6 8 : 3-34 Baaras Hidu Uiversity Varaasi ISS : 447-9483 Geeralized ad trasformed two phase samplig Ratio ad Product ype stimators for Populatio Mea Usig uiliary haracter
More informationAbstract. Ranked set sampling, auxiliary variable, variance.
Hacettepe Joural of Mathematics ad Statistics Volume (), 1 A class of Hartley-Ross type Ubiased estimators for Populatio Mea usig Raked Set Samplig Lakhkar Kha ad Javid Shabbir Abstract I this paper, we
More informationSYSTEMATIC SAMPLING FOR NON-LINEAR TREND IN MILK YIELD DATA
Joural of Reliability ad Statistical Studies; ISS (Prit): 0974-804, (Olie):9-5666 Vol. 7, Issue (04): 57-68 SYSTEMATIC SAMPLIG FOR O-LIEAR TRED I MILK YIELD DATA Tauj Kumar Padey ad Viod Kumar Departmet
More informationAlternative Ratio Estimator of Population Mean in Simple Random Sampling
Joural of Mathematics Research; Vol. 6, No. 3; 014 ISSN 1916-9795 E-ISSN 1916-9809 Published by Caadia Ceter of Sciece ad Educatio Alterative Ratio Estimator of Populatio Mea i Simple Radom Samplig Ekaette
More informationThe Sampling Distribution of the Maximum. Likelihood Estimators for the Parameters of. Beta-Binomial Distribution
Iteratioal Mathematical Forum, Vol. 8, 2013, o. 26, 1263-1277 HIKARI Ltd, www.m-hikari.com http://d.doi.org/10.12988/imf.2013.3475 The Samplig Distributio of the Maimum Likelihood Estimators for the Parameters
More informationRandom Variables, Sampling and Estimation
Chapter 1 Radom Variables, Samplig ad Estimatio 1.1 Itroductio This chapter will cover the most importat basic statistical theory you eed i order to uderstad the ecoometric material that will be comig
More informationAn Improved Warner s Randomized Response Model
Iteratioal Joural of Statistics ad Applicatios 05, 5(6: 63-67 DOI: 0.593/j.statistics.050506.0 A Improved Warer s Radomized Respose Model F. B. Adebola, O. O. Johso * Departmet of Statistics, Federal Uiversit
More informationJambulingam Subramani 1, Gnanasegaran Kumarapandiyan 2 and Saminathan Balamurali 3
ISSN 1684-8403 Joural of Statistics Volume, 015. pp. 84-305 Abstract A Class of Modified Liear Regressio Type Ratio Estimators for Estimatio of Populatio Mea usig Coefficiet of Variatio ad Quartiles of
More informationProperties and Hypothesis Testing
Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.
More informationAClassofRegressionEstimatorwithCumDualProductEstimatorAsIntercept
Global Joural of Sciece Frotier Research: F Mathematics ad Decisio Scieces Volume 15 Issue 3 Versio 1.0 Year 2015 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic.
More informationImprovement in Estimating The Population Mean Using Dual To Ratio-Cum-Product Estimator in Simple Random Sampling
Olufadi Yuusa Departmet of tatistics ad Mathematical cieces Kwara tate Uiversit.M.B 53 Malete Nigeria ajesh igh Departmet of tatistics Baaras Hidu Uiversit Varaasi (U..) Idia Floreti maradache Uiversit
More informationDeveloping Efficient Ratio and Product Type Exponential Estimators of Population Mean under Two Phase Sampling for Stratification
America Joural of Operatioal Researc 05 5: -8 DOI: 0.593/j.ajor.05050.0 Developig Efficiet Ratio ad Product Type Epoetial Eimators of Populatio Mea uder Two Pase Samplig for Stratificatio Subas Kumar adav
More informationIt should be unbiased, or approximately unbiased. Variance of the variance estimator should be small. That is, the variance estimator is stable.
Chapter 10 Variace Estimatio 10.1 Itroductio Variace estimatio is a importat practical problem i survey samplig. Variace estimates are used i two purposes. Oe is the aalytic purpose such as costructig
More informationGeneralized Exponential Type Estimator for Population Variance in Survey Sampling
Revista Colombiaa de Estadística Juio 2014, volume 37, o. 1, pp. 211 a 222 Geeralized Expoetial Type Estimator for Populatio Variace i Survey Samplig Estimadores tipo expoecial geeralizado para la variaza
More informationESTIMATION OF FINITE POPULATION MEAN WITH KNOWN COEFFICIENT OF VARIATION OF AN AUXILIARY CHARACTER
STATISTICA, ao LXV,. 3, 2005 ESTIMATION OF FINITE POPULATION MEAN WITH KNOWN COEFFICIENT OF VARIATION OF AN AUXILIAR CHARACTER H.P. Sigh, R. Tail 1. INTRODUCTION AND THE SUGGESTED ESTIMATOR It is well
More informationResearch Article An Alternative Estimator for Estimating the Finite Population Mean Using Auxiliary Information in Sample Surveys
Iteratioal Scholarly Research Network ISRN Probability ad Statistics Volume 01, Article ID 65768, 1 pages doi:10.50/01/65768 Research Article A Alterative Estimator for Estimatig the Fiite Populatio Mea
More informationImproved Ratio Estimators of Population Mean In Adaptive Cluster Sampling
J. Stat. Appl. Pro. Lett. 3, o. 1, 1-6 (016) 1 Joural of Statistics Applicatios & Probability Letters A Iteratioal Joural http://dx.doi.org/10.18576/jsapl/030101 Improved Ratio Estimators of Populatio
More informationG. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan
Deviatio of the Variaces of Classical Estimators ad Negative Iteger Momet Estimator from Miimum Variace Boud with Referece to Maxwell Distributio G. R. Pasha Departmet of Statistics Bahauddi Zakariya Uiversity
More informationElement sampling: Part 2
Chapter 4 Elemet samplig: Part 2 4.1 Itroductio We ow cosider uequal probability samplig desigs which is very popular i practice. I the uequal probability samplig, we ca improve the efficiecy of the resultig
More information1 Inferential Methods for Correlation and Regression Analysis
1 Iferetial Methods for Correlatio ad Regressio Aalysis I the chapter o Correlatio ad Regressio Aalysis tools for describig bivariate cotiuous data were itroduced. The sample Pearso Correlatio Coefficiet
More informationBootstrap Intervals of the Parameters of Lognormal Distribution Using Power Rule Model and Accelerated Life Tests
Joural of Moder Applied Statistical Methods Volume 5 Issue Article --5 Bootstrap Itervals of the Parameters of Logormal Distributio Usig Power Rule Model ad Accelerated Life Tests Mohammed Al-Ha Ebrahem
More informationA New Mixed Randomized Response Model
Iteratioal Joural of Busiess ad Social Sciece ol No ; October 00 A New Mixed adomized espose Model Aesha Nazuk NUST Busiess School Islamabad, Paksta E-mail: Aeshaazuk@bsedupk Phoe: 009-5-9085-367 Abstract
More informationInvestigating the Significance of a Correlation Coefficient using Jackknife Estimates
Iteratioal Joural of Scieces: Basic ad Applied Research (IJSBAR) ISSN 2307-4531 (Prit & Olie) http://gssrr.org/idex.php?joural=jouralofbasicadapplied ---------------------------------------------------------------------------------------------------------------------------
More informationDouble Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution
Iteratioal Mathematical Forum, Vol., 3, o. 3, 3-53 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.9/imf.3.335 Double Stage Shrikage Estimator of Two Parameters Geeralized Expoetial Distributio Alaa M.
More informationSimple Random Sampling!
Simple Radom Samplig! Professor Ro Fricker! Naval Postgraduate School! Moterey, Califoria! Readig:! 3/26/13 Scheaffer et al. chapter 4! 1 Goals for this Lecture! Defie simple radom samplig (SRS) ad discuss
More informationA statistical method to determine sample size to estimate characteristic value of soil parameters
A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig
More informationEDGEWORTH SIZE CORRECTED W, LR AND LM TESTS IN THE FORMATION OF THE PRELIMINARY TEST ESTIMATOR
Joural of Statistical Research 26, Vol. 37, No. 2, pp. 43-55 Bagladesh ISSN 256-422 X EDGEORTH SIZE CORRECTED, AND TESTS IN THE FORMATION OF THE PRELIMINARY TEST ESTIMATOR Zahirul Hoque Departmet of Statistics
More informationComparison of Minimum Initial Capital with Investment and Non-investment Discrete Time Surplus Processes
The 22 d Aual Meetig i Mathematics (AMM 207) Departmet of Mathematics, Faculty of Sciece Chiag Mai Uiversity, Chiag Mai, Thailad Compariso of Miimum Iitial Capital with Ivestmet ad -ivestmet Discrete Time
More informationMATH 320: Probability and Statistics 9. Estimation and Testing of Parameters. Readings: Pruim, Chapter 4
MATH 30: Probability ad Statistics 9. Estimatio ad Testig of Parameters Estimatio ad Testig of Parameters We have bee dealig situatios i which we have full kowledge of the distributio of a radom variable.
More information7-1. Chapter 4. Part I. Sampling Distributions and Confidence Intervals
7-1 Chapter 4 Part I. Samplig Distributios ad Cofidece Itervals 1 7- Sectio 1. Samplig Distributio 7-3 Usig Statistics Statistical Iferece: Predict ad forecast values of populatio parameters... Test hypotheses
More informationExpectation and Variance of a random variable
Chapter 11 Expectatio ad Variace of a radom variable The aim of this lecture is to defie ad itroduce mathematical Expectatio ad variace of a fuctio of discrete & cotiuous radom variables ad the distributio
More informationINF Introduction to classifiction Anne Solberg Based on Chapter 2 ( ) in Duda and Hart: Pattern Classification
INF 4300 90 Itroductio to classifictio Ae Solberg ae@ifiuioo Based o Chapter -6 i Duda ad Hart: atter Classificatio 90 INF 4300 Madator proect Mai task: classificatio You must implemet a classificatio
More informationREVISTA INVESTIGACION OPERACIONAL VOL. 35, NO. 1, 49-57, 2014
EVISTA IVESTIGAIO OPEAIOAL VOL. 35, O., 9-57, 0 O A IMPOVED ATIO TYPE ESTIMATO OF FIITE POPULATIO MEA I SAMPLE SUVEYS A K P Swai Former Professor of Statistics, Utkal Uiversit, Bhubaeswar-7500, Idia ABSTAT
More informationA Generalized Class of Unbiased Estimators for Population Mean Using Auxiliary Information on an Attribute and an Auxiliary Variable
Iteratioal Joural of Computatioal ad Applied Mathematics. ISSN 89-4966 Volume, Number 07, pp. -8 Research Idia ublicatios http://www.ripublicatio.com A Geeralized Class of Ubiased Estimators for opulatio
More informationHypothesis Testing. Evaluation of Performance of Learned h. Issues. Trade-off Between Bias and Variance
Hypothesis Testig Empirically evaluatig accuracy of hypotheses: importat activity i ML. Three questios: Give observed accuracy over a sample set, how well does this estimate apply over additioal samples?
More informationEstimation of Population Mean in Presence of Non-Response in Double Sampling
J. Stat. Appl. Pro. 6, No. 2, 345-353 (2017) 345 Joural of Statistics Applicatios & Probability A Iteratioal Joural http://dx.doi.org/10.18576/jsap/060209 Estimatio of Populatio Mea i Presece of No-Respose
More informationECE 901 Lecture 12: Complexity Regularization and the Squared Loss
ECE 90 Lecture : Complexity Regularizatio ad the Squared Loss R. Nowak 5/7/009 I the previous lectures we made use of the Cheroff/Hoeffdig bouds for our aalysis of classifier errors. Hoeffdig s iequality
More informationGUIDELINES ON REPRESENTATIVE SAMPLING
DRUGS WORKING GROUP VALIDATION OF THE GUIDELINES ON REPRESENTATIVE SAMPLING DOCUMENT TYPE : REF. CODE: ISSUE NO: ISSUE DATE: VALIDATION REPORT DWG-SGL-001 002 08 DECEMBER 2012 Ref code: DWG-SGL-001 Issue
More informationUniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations
Global Joural of Sciece Frotier Research Mathematics ad Decisio Scieces Volume 3 Issue Versio 0 Year 03 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic (USA Olie
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 5
CS434a/54a: Patter Recogitio Prof. Olga Veksler Lecture 5 Today Itroductio to parameter estimatio Two methods for parameter estimatio Maimum Likelihood Estimatio Bayesia Estimatio Itroducto Bayesia Decisio
More informationON POINTWISE BINOMIAL APPROXIMATION
Iteratioal Joural of Pure ad Applied Mathematics Volume 71 No. 1 2011, 57-66 ON POINTWISE BINOMIAL APPROXIMATION BY w-functions K. Teerapabolar 1, P. Wogkasem 2 Departmet of Mathematics Faculty of Sciece
More informationDual to Ratio Estimators for Mean Estimation in Successive Sampling using Auxiliary Information on Two Occasion
J. Stat. Appl. Pro. 7, o. 1, 49-58 (018) 49 Joural of Statistics Applicatios & Probability A Iteratioal Joural http://dx.doi.org/10.18576/jsap/070105 Dual to Ratio Estimators for Mea Estimatio i Successive
More informationPOWER AKASH DISTRIBUTION AND ITS APPLICATION
POWER AKASH DISTRIBUTION AND ITS APPLICATION Rama SHANKER PhD, Uiversity Professor, Departmet of Statistics, College of Sciece, Eritrea Istitute of Techology, Asmara, Eritrea E-mail: shakerrama009@gmail.com
More informationLecture 22: Review for Exam 2. 1 Basic Model Assumptions (without Gaussian Noise)
Lecture 22: Review for Exam 2 Basic Model Assumptios (without Gaussia Noise) We model oe cotiuous respose variable Y, as a liear fuctio of p umerical predictors, plus oise: Y = β 0 + β X +... β p X p +
More informationLinear Regression Models
Liear Regressio Models Dr. Joh Mellor-Crummey Departmet of Computer Sciece Rice Uiversity johmc@cs.rice.edu COMP 528 Lecture 9 15 February 2005 Goals for Today Uderstad how to Use scatter diagrams to ispect
More informationTopic 5 [434 marks] (i) Find the range of values of n for which. (ii) Write down the value of x dx in terms of n, when it does exist.
Topic 5 [44 marks] 1a (i) Fid the rage of values of for which eists 1 Write dow the value of i terms of 1, whe it does eist Fid the solutio to the differetial equatio 1b give that y = 1 whe = π (cos si
More informationResearch Article A Two-Parameter Ratio-Product-Ratio Estimator Using Auxiliary Information
Iteratioal Scholarly Research Network ISRN Probability ad Statistics Volume, Article ID 386, 5 pages doi:.54//386 Research Article A Two-Parameter Ratio-Product-Ratio Estimator Usig Auxiliary Iformatio
More informationModeling and Estimation of a Bivariate Pareto Distribution using the Principle of Maximum Entropy
Sri Laka Joural of Applied Statistics, Vol (5-3) Modelig ad Estimatio of a Bivariate Pareto Distributio usig the Priciple of Maximum Etropy Jagathath Krisha K.M. * Ecoomics Research Divisio, CSIR-Cetral
More information[ ] ( ) ( ) [ ] ( ) 1 [ ] [ ] Sums of Random Variables Y = a 1 X 1 + a 2 X 2 + +a n X n The expected value of Y is:
PROBABILITY FUNCTIONS A radom variable X has a probabilit associated with each of its possible values. The probabilit is termed a discrete probabilit if X ca assume ol discrete values, or X = x, x, x 3,,
More informationMaximum likelihood estimation from record-breaking data for the generalized Pareto distribution
METRON - Iteratioal Joural of Statistics 004, vol. LXII,. 3, pp. 377-389 NAGI S. ABD-EL-HAKIM KHALAF S. SULTAN Maximum likelihood estimatio from record-breakig data for the geeralized Pareto distributio
More informationECONOMETRIC THEORY. MODULE XIII Lecture - 34 Asymptotic Theory and Stochastic Regressors
ECONOMETRIC THEORY MODULE XIII Lecture - 34 Asymptotic Theory ad Stochastic Regressors Dr. Shalabh Departmet of Mathematics ad Statistics Idia Istitute of Techology Kapur Asymptotic theory The asymptotic
More informationOn stratified randomized response sampling
Model Assisted Statistics ad Applicatios 1 (005,006) 31 36 31 IOS ress O stratified radomized respose samplig Jea-Bok Ryu a,, Jog-Mi Kim b, Tae-Youg Heo c ad Chu Gu ark d a Statistics, Divisio of Life
More informationf(x i ; ) L(x; p) = i=1 To estimate the value of that maximizes L or equivalently ln L we will set =0, for i =1, 2,...,m p x i (1 p) 1 x i i=1
Parameter Estimatio Samples from a probability distributio F () are: [,,..., ] T.Theprobabilitydistributio has a parameter vector [,,..., m ] T. Estimator: Statistic used to estimate ukow. Estimate: Observed
More informationAn Introduction to Randomized Algorithms
A Itroductio to Radomized Algorithms The focus of this lecture is to study a radomized algorithm for quick sort, aalyze it usig probabilistic recurrece relatios, ad also provide more geeral tools for aalysis
More information5. Fractional Hot deck Imputation
5. Fractioal Hot deck Imputatio Itroductio Suppose that we are iterested i estimatig θ EY or eve θ 2 P ry < c where y fy x where x is always observed ad y is subject to missigess. Assume MAR i the sese
More informationAccess to the published version may require journal subscription. Published with permission from: Elsevier.
This is a author produced versio of a paper published i Statistics ad Probability Letters. This paper has bee peer-reviewed, it does ot iclude the joural pagiatio. Citatio for the published paper: Forkma,
More informationSolutions to Odd Numbered End of Chapter Exercises: Chapter 4
Itroductio to Ecoometrics (3 rd Updated Editio) by James H. Stock ad Mark W. Watso Solutios to Odd Numbered Ed of Chapter Exercises: Chapter 4 (This versio July 2, 24) Stock/Watso - Itroductio to Ecoometrics
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 9 Multicolliearity Dr Shalabh Departmet of Mathematics ad Statistics Idia Istitute of Techology Kapur Multicolliearity diagostics A importat questio that
More informationJournal of Reliability and Statistical Studies; ISSN (Print): , (Online): Vol. 11, Issue 1 (2018): 51-66
Joral of Reliabilit ad Statistical Stdies; ISS (Prit: 0974-804, (Olie: 9 5666 Vol., Isse (08: 5-66 ESTIMATIO OF FIITE POPULATIO MEA USIG KOW OEFFIIET OF VARIATIO I THE SIMULTAEOUS PRESEE OF O - RESPOSE
More information3/3/2014. CDS M Phil Econometrics. Types of Relationships. Types of Relationships. Types of Relationships. Vijayamohanan Pillai N.
3/3/04 CDS M Phil Old Least Squares (OLS) Vijayamohaa Pillai N CDS M Phil Vijayamoha CDS M Phil Vijayamoha Types of Relatioships Oly oe idepedet variable, Relatioship betwee ad is Liear relatioships Curviliear
More informationEstimation for Complete Data
Estimatio for Complete Data complete data: there is o loss of iformatio durig study. complete idividual complete data= grouped data A complete idividual data is the oe i which the complete iformatio of
More informationUnbiased Estimation. February 7-12, 2008
Ubiased Estimatio February 7-2, 2008 We begi with a sample X = (X,..., X ) of radom variables chose accordig to oe of a family of probabilities P θ where θ is elemet from the parameter space Θ. For radom
More informationECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015
ECE 8527: Itroductio to Machie Learig ad Patter Recogitio Midterm # 1 Vaishali Ami Fall, 2015 tue39624@temple.edu Problem No. 1: Cosider a two-class discrete distributio problem: ω 1 :{[0,0], [2,0], [2,2],
More informationMOMENT-METHOD ESTIMATION BASED ON CENSORED SAMPLE
Vol. 8 o. Joural of Systems Sciece ad Complexity Apr., 5 MOMET-METHOD ESTIMATIO BASED O CESORED SAMPLE I Zhogxi Departmet of Mathematics, East Chia Uiversity of Sciece ad Techology, Shaghai 37, Chia. Email:
More informationEXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY
EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA, 016 MODULE : Statistical Iferece Time allowed: Three hours Cadidates should aswer FIVE questios. All questios carry equal marks. The umber
More informationOn ratio and product methods with certain known population parameters of auxiliary variable in sample surveys
Statistics & Operatios Research Trasactios SORT 34 July-December 010, 157-180 ISSN: 1696-81 www.idescat.cat/sort/ Statistics & Operatios Research c Istitut d Estadística de Cataluya Trasactios sort@idescat.cat
More informationLecture 2: Monte Carlo Simulation
STAT/Q SCI 43: Itroductio to Resamplig ethods Sprig 27 Istructor: Ye-Chi Che Lecture 2: ote Carlo Simulatio 2 ote Carlo Itegratio Assume we wat to evaluate the followig itegratio: e x3 dx What ca we do?
More informationEconomics 241B Relation to Method of Moments and Maximum Likelihood OLSE as a Maximum Likelihood Estimator
Ecoomics 24B Relatio to Method of Momets ad Maximum Likelihood OLSE as a Maximum Likelihood Estimator Uder Assumptio 5 we have speci ed the distributio of the error, so we ca estimate the model parameters
More informationMA Advanced Econometrics: Properties of Least Squares Estimators
MA Advaced Ecoometrics: Properties of Least Squares Estimators Karl Whela School of Ecoomics, UCD February 5, 20 Karl Whela UCD Least Squares Estimators February 5, 20 / 5 Part I Least Squares: Some Fiite-Sample
More informationApproximate Confidence Interval for the Reciprocal of a Normal Mean with a Known Coefficient of Variation
Metodološki zvezki, Vol. 13, No., 016, 117-130 Approximate Cofidece Iterval for the Reciprocal of a Normal Mea with a Kow Coefficiet of Variatio Wararit Paichkitkosolkul 1 Abstract A approximate cofidece
More informationChapter 6 Sampling Distributions
Chapter 6 Samplig Distributios 1 I most experimets, we have more tha oe measuremet for ay give variable, each measuremet beig associated with oe radomly selected a member of a populatio. Hece we eed to
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More informationCorrelation Regression
Correlatio Regressio While correlatio methods measure the stregth of a liear relatioship betwee two variables, we might wish to go a little further: How much does oe variable chage for a give chage i aother
More informationCastiel, Supernatural, Season 6, Episode 18
13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio
More information5.4 The spatial error model Regression model with spatially autocorrelated errors
54 The spatial error model 54 Regressio model with spatiall autocorrelated errors I a multiple regressio model, the depedet variable Y depeds o k regressors X (=), X,, X k ad a disturbace ε: (4) is a x
More informationNew Entropy Estimators with Smaller Root Mean Squared Error
Joural of Moder Applied Statistical Methods Volume 4 Issue 2 Article 0 --205 New Etropy Estimators with Smaller Root Mea Squared Error Amer Ibrahim Al-Omari Al al-bayt Uiversity, Mafraq, Jorda, alomari_amer@yahoo.com
More informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals
More informationFinite Difference Approximation for Transport Equation with Shifts Arising in Neuronal Variability
Iteratioal Joural of Sciece ad Research (IJSR) ISSN (Olie): 39-764 Ide Copericus Value (3): 64 Impact Factor (3): 4438 Fiite Differece Approimatio for Trasport Equatio with Shifts Arisig i Neuroal Variability
More informationA Note on Box-Cox Quantile Regression Estimation of the Parameters of the Generalized Pareto Distribution
A Note o Box-Cox Quatile Regressio Estimatio of the Parameters of the Geeralized Pareto Distributio JM va Zyl Abstract: Makig use of the quatile equatio, Box-Cox regressio ad Laplace distributed disturbaces,
More informationBayesian and E- Bayesian Method of Estimation of Parameter of Rayleigh Distribution- A Bayesian Approach under Linex Loss Function
Iteratioal Joural of Statistics ad Systems ISSN 973-2675 Volume 12, Number 4 (217), pp. 791-796 Research Idia Publicatios http://www.ripublicatio.com Bayesia ad E- Bayesia Method of Estimatio of Parameter
More informationMathematical Modeling of Optimum 3 Step Stress Accelerated Life Testing for Generalized Pareto Distribution
America Joural of Theoretical ad Applied Statistics 05; 4(: 6-69 Published olie May 8, 05 (http://www.sciecepublishiggroup.com/j/ajtas doi: 0.648/j.ajtas.05040. ISSN: 6-8999 (Prit; ISSN: 6-9006 (Olie Mathematical
More informationFinite Difference Approximation for First- Order Hyperbolic Partial Differential Equation Arising in Neuronal Variability with Shifts
Iteratioal Joural of Scietific Egieerig ad Research (IJSER) wwwiseri ISSN (Olie): 347-3878, Impact Factor (4): 35 Fiite Differece Approimatio for First- Order Hyperbolic Partial Differetial Equatio Arisig
More information