Testing Statistical Hypotheses


 Cameron Jackson
 1 years ago
 Views:
Transcription
1 E.L. Lehmann Joseph P. Romano Testing Statistical Hypotheses Third Edition 4y Springer
2 Preface vii I SmallSample Theory 1 1 The General Decision Problem Statistical Inference and Statistical Decisions Specification of a Decision Problem Randomization; Choice of Experiment Optimum Procedures Invariance and Unbiasedness ll 1.6 Bayes and Minimax Procedures Maximum Likelihood Iβ 1.8 Complete Classes Sufficient Statistics IS 1.10 Problems LM 1.1 I Notes 27 2 The Probability Background 28 2t Probability and Measure 2 S 2.2 Integration Statistics and Subfields Conditional Expectation and Probability Conditional Probability Distributions Characterization of Sufficiency Exponential Families 46
3 2.8 Problems 2.9 Notes Uniformly Most Powerful Tests Stating The Problem The NeymanPearson Fundamental Lemma pvalues Distributions with Monotone Likelihood Ratio Confidence Bounds A Generalization of the Fundamental Lemma TwoSided Hypotheses Least Favorable Distributions Applications to Normal Distributions Univariate Normal Models Multivariate Normal Models Problems Notes 107 Unbiasedness: Theory and First Applications Unbiasedness For Hypothesis Testing OneParameter Exponential Families Ill 4.3 Similarity and Completeness UMP Unbiased Tests for Multiparameter Exponential Families Comparing Two Poisson or Binomial Populations Testing for Independence in a 2 x 2 Table Alternative Models for 2 x 2 Tables Some ThreeFactor Contingency Tables The Sign Test Problems Notes 149 Unbiasedness: Applications to Normal Distributions Statistics Independent of a Sufficient Statistic Testing the Parameters of a Normal Distribution Comparing the Means and Variances of Two Normal Distributions Confidence Intervals and Families of Tests Unbiased Confidence Sets 1G4 5.0 Regression Bayesian Confidence Sets Permutation Tests Most Powerful Permutation Tests Randomization As A Basis For Inference Permutation Tests and Randomization Randomization Model and Confidence Intervals Testing for Independence in a Bivariate Normal Distribution Problems Notes 210
4 xi 6 Invariance Symmetry and Invariance Maximal Invariants Most Powerful Invariant Tests Sample Inspection by Variables Almost Invariance Unbiasedness and Invariance Admissibility Rank Tests The TwoSample Problem The Hypothesis of Symmetry Equivariant Confidence Sets Average Smallest Equivariant Confidence Sets Confidence Bands for a Distribution Function Problems Notes Linear Hypotheses A Canonical Form Linear Hypotheses and Least Squares Tests of Homogeneity TwoWay Layout: One Observation per Cell TwoWay Layout: m Observations Per Cell Regression RandomEffects Model: Oneway Classification Nested Classifications Multivariate Extensions Problems Notes The Minimax Principle Tests with Guaranteed Power Examples Comparing Two Approximate Hypotheses Maximin Tests and Invariance The Hunt Stein Theorem Most Stringent Tests Problems Notes Multiple Testing and Simultaneous Inference Introduction and the FWER Maximin Procedures The Hypothesis of Homogeneity Scheffé's 5Method: A Special Case Scheffé's SMethod for General Linear Models Problems Notes 391
5 xii Contents 10 Conditional Inference Mixtures of Experiments Ancillary Statistics Optimal Conditional Tests Relevant Subsets Problems Notes 414 II LargeSample Theory Basic Large Sample Theory Introduction Basic Convergence Concepts Weak Convergence and Central Limit Theorems Convergence in Probability and Applications Almost Sure Convergence Robustness of Some Classical Tests Effect of Distribution Effect of Dependence Robustness in Linear Models Nonparametric Mean Edgeworth Expansions The ttest A Result of Bahadur and Savage Alternative Tests Problems Notes Quadratic Mean Differentiable Families Introduction Quadratic Mean Differentiability (q.m.d.) Contiguity Likelihood Methods in Parametric Models Efficient Likelihood Estimation Wald Tests and Confidence Regions Rao Score Tests Likelihood Ratio Tests Problems Notes Large Sample Optimality Testing Sequences, Metrics, and Inequalities Asymptotic Relative Efficiency AUMP Tests in Univariate Models Asymptotically Normal Experiments Applications to Parametric Models Onesided Hypotheses Equivalence Hypotheses 559
6 xiii Multisided Hypotheses Applications to Nonparametric Models Nonparametric Mean Nonparametric Testing of Functionals Problems Notes Testing Goodness of Fit Introduction The KolmogorovSmirnov Test Simple Null Hypothesis Extensions of the KolmogorovSmirnov Test Pearson's Chisquared Statistic Simple Null Hypothesis Chisquared Test of Uniformity Composite Null Hypothesis Neyman's Smooth Tests Fixed k Asymptotics Neyman's Smooth Tests With Large k Weighted Quadratic Test Statistics Global Behavior of Power Functions Problems Notes General Large Sample Methods Introduction Permutation and Randomization Tests The Basic Construction Asymptotic Results Basic Large Sample Approximations Pivotal Method Asymptotic Pivotal Method Asymptotic Approximation Bootstrap Sampling Distributions Introduction and Consistency The Nonparametric Mean Further Examples Stepdown Multiple Testing Higher Order Asymptotic Comparisons Hypothesis Testing Subsampling The Basic Theorem in the I.I.D. Case Comparison with the Bootstrap Hypothesis Testing Problems Notes 690 A Auxiliary Results 692 A.l Equivalence Relations; Groups 592
7 xiv Contents A.2 Convergence of Functions; Metric Spaces 693 A.3 Banach and Hilbert Spaces 696 A.4 Dominated Families of Distributions 698 A.5 The Weak Compactness Theorem 700 References 702 Author Index 757 Subject Index 767
Testing Statistical Hypotheses
E.L. Lehmann Joseph P. Romano, 02LEu1 ttd ~Lt~S Testing Statistical Hypotheses Third Edition With 6 Illustrations ~Springer 2 The Probability Background 28 2.1 Probability and Measure 28 2.2 Integration.........
More informationPRINCIPLES OF STATISTICAL INFERENCE
Advanced Series on Statistical Science & Applied Probability PRINCIPLES OF STATISTICAL INFERENCE from a NeoFisherian Perspective Luigi Pace Department of Statistics University ofudine, Italy Alessandra
More informationStatistical Methods in HYDROLOGY CHARLES T. HAAN. The Iowa State University Press / Ames
Statistical Methods in HYDROLOGY CHARLES T. HAAN The Iowa State University Press / Ames Univariate BASIC Table of Contents PREFACE xiii ACKNOWLEDGEMENTS xv 1 INTRODUCTION 1 2 PROBABILITY AND PROBABILITY
More informationStat 5101 Lecture Notes
Stat 5101 Lecture Notes Charles J. Geyer Copyright 1998, 1999, 2000, 2001 by Charles J. Geyer May 7, 2001 ii Stat 5101 (Geyer) Course Notes Contents 1 Random Variables and Change of Variables 1 1.1 Random
More informationPART I INTRODUCTION The meaning of probability Basic definitions for frequentist statistics and Bayesian inference Bayesian inference Combinatorics
Table of Preface page xi PART I INTRODUCTION 1 1 The meaning of probability 3 1.1 Classical definition of probability 3 1.2 Statistical definition of probability 9 1.3 Bayesian understanding of probability
More informationTheory and Methods of Statistical Inference. PART I Frequentist theory and methods
PhD School in Statistics cycle XXVI, 2011 Theory and Methods of Statistical Inference PART I Frequentist theory and methods (A. Salvan, N. Sartori, L. Pace) Syllabus Some prerequisites: Empirical distribution
More informationTheory and Methods of Statistical Inference
PhD School in Statistics cycle XXIX, 2014 Theory and Methods of Statistical Inference Instructors: B. Liseo, L. Pace, A. Salvan (course coordinator), N. Sartori, A. Tancredi, L. Ventura Syllabus Some prerequisites:
More informationTheory and Methods of Statistical Inference. PART I Frequentist likelihood methods
PhD School in Statistics XXV cycle, 2010 Theory and Methods of Statistical Inference PART I Frequentist likelihood methods (A. Salvan, N. Sartori, L. Pace) Syllabus Some prerequisites: Empirical distribution
More informationThe University of Hong Kong Department of Statistics and Actuarial Science STAT2802 Statistical Models Tutorial Solutions Solutions to Problems 7180
The University of Hong Kong Department of Statistics and Actuarial Science STAT2802 Statistical Models Tutorial Solutions Solutions to Problems 7180 71. Decide in each case whether the hypothesis is simple
More informationSubjective and Objective Bayesian Statistics
Subjective and Objective Bayesian Statistics Principles, Models, and Applications Second Edition S. JAMES PRESS with contributions by SIDDHARTHA CHIB MERLISE CLYDE GEORGE WOODWORTH ALAN ZASLAVSKY \WILEY
More informationHypothesis Testing. 1 Definitions of test statistics. CB: chapter 8; section 10.3
Hypothesis Testing CB: chapter 8; section 0.3 Hypothesis: statement about an unknown population parameter Examples: The average age of males in Sweden is 7. (statement about population mean) The lowest
More informationNumerical Analysis for Statisticians
Kenneth Lange Numerical Analysis for Statisticians Springer Contents Preface v 1 Recurrence Relations 1 1.1 Introduction 1 1.2 Binomial CoefRcients 1 1.3 Number of Partitions of a Set 2 1.4 Horner's Method
More informationParametric Inference Maximum Likelihood Inference Exponential Families Expectation Maximization (EM) Bayesian Inference Statistical Decison Theory
Statistical Inference Parametric Inference Maximum Likelihood Inference Exponential Families Expectation Maximization (EM) Bayesian Inference Statistical Decison Theory IP, José Bioucas Dias, IST, 2007
More informationDESIGNING EXPERIMENTS AND ANALYZING DATA A Model Comparison Perspective
DESIGNING EXPERIMENTS AND ANALYZING DATA A Model Comparison Perspective Second Edition Scott E. Maxwell Uniuersity of Notre Dame Harold D. Delaney Uniuersity of New Mexico J,t{,.?; LAWRENCE ERLBAUM ASSOCIATES,
More informationTime Series Analysis. James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY
Time Series Analysis James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY & Contents PREFACE xiii 1 1.1. 1.2. Difference Equations FirstOrder Difference Equations 1 /?thorder Difference
More informationLessons in Estimation Theory for Signal Processing, Communications, and Control
Lessons in Estimation Theory for Signal Processing, Communications, and Control Jerry M. Mendel Department of Electrical Engineering University of Southern California Los Angeles, California PRENTICE HALL
More informationA Very Brief Summary of Statistical Inference, and Examples
A Very Brief Summary of Statistical Inference, and Examples Trinity Term 2009 Prof. Gesine Reinert Our standard situation is that we have data x = x 1, x 2,..., x n, which we view as realisations of random
More informationGeneralized Multivariate Rank Type Test Statistics via Spatial UQuantiles
Generalized Multivariate Rank Type Test Statistics via Spatial UQuantiles Weihua Zhou 1 University of North Carolina at Charlotte and Robert Serfling 2 University of Texas at Dallas Final revision for
More informationLinear Models 1. Isfahan University of Technology Fall Semester, 2014
Linear Models 1 Isfahan University of Technology Fall Semester, 2014 References: [1] G. A. F., Seber and A. J. Lee (2003). Linear Regression Analysis (2nd ed.). Hoboken, NJ: Wiley. [2] A. C. Rencher and
More informationWiley. Methods and Applications of Linear Models. Regression and the Analysis. of Variance. Third Edition. Ishpeming, Michigan RONALD R.
Methods and Applications of Linear Models Regression and the Analysis of Variance Third Edition RONALD R. HOCKING PenHock Statistical Consultants Ishpeming, Michigan Wiley Contents Preface to the Third
More informationChapter 4 HOMEWORK ASSIGNMENTS. 4.1 Homework #1
Chapter 4 HOMEWORK ASSIGNMENTS These homeworks may be modified as the semester progresses. It is your responsibility to keep up to date with the correctly assigned homeworks. There may be some errors in
More informationHYPOTHESIS TESTING: FREQUENTIST APPROACH.
HYPOTHESIS TESTING: FREQUENTIST APPROACH. These notes summarize the lectures on (the frequentist approach to) hypothesis testing. You should be familiar with the standard hypothesis testing from previous
More informationHypothesis Testing. A rule for making the required choice can be described in two ways: called the rejection or critical region of the test.
Hypothesis Testing Hypothesis testing is a statistical problem where you must choose, on the basis of data X, between two alternatives. We formalize this as the problem of choosing between two hypotheses:
More informationPATTERN CLASSIFICATION
PATTERN CLASSIFICATION Second Edition Richard O. Duda Peter E. Hart David G. Stork A Wileylnterscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Singapore Toronto CONTENTS
More informationFrom Practical Data Analysis with JMP, Second Edition. Full book available for purchase here. About This Book... xiii About The Author...
From Practical Data Analysis with JMP, Second Edition. Full book available for purchase here. Contents About This Book... xiii About The Author... xxiii Chapter 1 Getting Started: Data Analysis with JMP...
More information14.30 Introduction to Statistical Methods in Economics Spring 2009
MIT OpenCourseWare http://ocw.mit.edu 4.0 Introduction to Statistical Methods in Economics Spring 009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationCh. 5 Hypothesis Testing
Ch. 5 Hypothesis Testing The current framework of hypothesis testing is largely due to the work of Neyman and Pearson in the late 1920s, early 30s, complementing Fisher s work on estimation. As in estimation,
More informationECE531 Lecture 4b: Composite Hypothesis Testing
ECE531 Lecture 4b: Composite Hypothesis Testing D. Richard Brown III Worcester Polytechnic Institute 16February2011 Worcester Polytechnic Institute D. Richard Brown III 16February2011 1 / 44 Introduction
More informationPATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS Parametric Distributions Basic building blocks: Need to determine given Representation: or? Recall Curve Fitting Binary Variables
More informationCHRIST UNIVERSITY HOSUR ROAD, BANGALORE
CHRIST UNIVERSITY HOSUR ROAD, BANGALORE  560 029 DEPARTMENT OF STATISTICS SYLLABUS FOR BSc STATISTICS Course Objectives The main objectives of this course are To acquaint students with various statistical
More informationMaximum Likelihood (ML) Estimation
Econometrics 2 Fall 2004 Maximum Likelihood (ML) Estimation Heino Bohn Nielsen 1of32 Outline of the Lecture (1) Introduction. (2) ML estimation defined. (3) ExampleI:Binomialtrials. (4) Example II: Linear
More informationSTATISTICS ( CODE NO. 08 ) PAPER I PART  I
STATISTICS ( CODE NO. 08 ) PAPER I PART  I 1. Descriptive Statistics Types of data  Concepts of a Statistical population and sample from a population ; qualitative and quantitative data ; nominal and
More informationUniversity of California San Diego and Stanford University and
First International Workshop on Functional and Operatorial Statistics. Toulouse, June 1921, 2008 Ksample Subsampling Dimitris N. olitis andjoseph.romano University of California San Diego and Stanford
More informationApplication of Variance Homogeneity Tests Under Violation of Normality Assumption
Application of Variance Homogeneity Tests Under Violation of Normality Assumption Alisa A. Gorbunova, Boris Yu. Lemeshko Novosibirsk State Technical University Novosibirsk, Russia email: gorbunova.alisa@gmail.com
More informationHypothesis testing:power, test statistic CMS:
Hypothesis testing:power, test statistic The more sensitive the test, the better it can discriminate between the null and the alternative hypothesis, quantitatively, maximal power In order to achieve this
More informationSCHEME OF EXAMINATION
APPENDIX AE28 MANONMANIAM SUNDARANAR UNIVERSITY, TIRUNELVELI 12. DIRECTORATE OF DISTANCE AND CONTINUING EDUCATION POSTGRADUATE DIPLOMA IN STATISTICAL METHODS AND APPLICATIONS (Effective from the Academic
More informationDirection: This test is worth 250 points and each problem worth points. DO ANY SIX
Term Test 3 December 5, 2003 Name Math 52 Student Number Direction: This test is worth 250 points and each problem worth 4 points DO ANY SIX PROBLEMS You are required to complete this test within 50 minutes
More informationStatistical and Inductive Inference by Minimum Message Length
C.S. Wallace Statistical and Inductive Inference by Minimum Message Length With 22 Figures Springer Contents Preface 1. Inductive Inference 1 1.1 Introduction 1 1.2 Inductive Inference 5 1.3 The Demise
More informationStatistics 135 Fall 2008 Final Exam
Name: SID: Statistics 135 Fall 2008 Final Exam Show your work. The number of points each question is worth is shown at the beginning of the question. There are 10 problems. 1. [2] The normal equations
More informationMathematical Statistics Old School
Mathematical Statistics Old School John I. Marden Department of Statistics University of Illinois at UrbanaChampaign 2017 by John I. Marden Email: mathematical@stat.istics.net URL: http://stat.istics.net/mathstat
More informationFundamentals of Statistical Signal Processing Volume II Detection Theory
Fundamentals of Statistical Signal Processing Volume II Detection Theory Steven M. Kay University of Rhode Island PH PTR Prentice Hall PTR Upper Saddle River, New Jersey 07458 http://www.phptr.com Contents
More information* Tuesday 17 January :3016:30 (2 hours) Recored on ESSE3 General introduction to the course.
Name of the course Statistical methods and data analysis Audience The course is intended for students of the first or second year of the Graduate School in Materials Engineering. The aim of the course
More informationThe Adequate Bootstrap
The Adequate Bootstrap arxiv:1608.05913v1 [stat.me] 21 Aug 2016 Toby Kenney Department of Mathematics and Statistics, Dalhousie University and Hong Gu Department of Mathematics and Statistics, Dalhousie
More informationSequential Procedure for Testing Hypothesis about Mean of Latent Gaussian Process
Applied Mathematical Sciences, Vol. 4, 2010, no. 62, 30833093 Sequential Procedure for Testing Hypothesis about Mean of Latent Gaussian Process Julia Bondarenko HelmutSchmidt University Hamburg University
More informationLarge Sample Properties of Estimators in the Classical Linear Regression Model
Large Sample Properties of Estimators in the Classical Linear Regression Model 7 October 004 A. Statement of the classical linear regression model The classical linear regression model can be written in
More information1. (Regular) Exponential Family
1. (Regular) Exponential Family The density function of a regular exponential family is: [ ] Example. Poisson(θ) [ ] Example. Normal. (both unknown). ) [ ] [ ] [ ] [ ] 2. Theorem (Exponential family &
More informationSupport Vector Method for Multivariate Density Estimation
Support Vector Method for Multivariate Density Estimation Vladimir N. Vapnik Royal Halloway College and AT &T Labs, 100 Schultz Dr. Red Bank, NJ 07701 vlad@research.att.com Sayan Mukherjee CBCL, MIT E25201
More informationAn Introduction to Applied Multivariate Analysis with R
~ Snrinuer Brian Everitt Torsten Hathorn An Introduction to Applied Multivariate Analysis with R > Preface........................................................ vii 1 Multivariate Data and Multivariate
More informationContents. 2 Sequences and Series Approximation by Rational Numbers Sequences Basics on Sequences...
Contents 1 Real Numbers: The Basics... 1 1.1 Notation... 1 1.2 Natural Numbers... 4 1.3 Integers... 5 1.4 Fractions and Rational Numbers... 10 1.4.1 Introduction... 10 1.4.2 Powers and Radicals of Rational
More informationTime Series: Theory and Methods
Peter J. Brockwell Richard A. Davis Time Series: Theory and Methods Second Edition With 124 Illustrations Springer Contents Preface to the Second Edition Preface to the First Edition vn ix CHAPTER 1 Stationary
More informationIDL Advanced Math & Stats Module
IDL Advanced Math & Stats Module Regression List of Routines and Functions Multiple Linear Regression IMSL_REGRESSORS IMSL_MULTIREGRESS IMSL_MULTIPREDICT Generates regressors for a general linear model.
More informationKarlRudolf Koch Introduction to Bayesian Statistics Second Edition
KarlRudolf Koch Introduction to Bayesian Statistics Second Edition KarlRudolf Koch Introduction to Bayesian Statistics Second, updated and enlarged Edition With 17 Figures Professor Dr.Ing., Dr.Ing.
More informationChapter 1 Statistical Inference
Chapter 1 Statistical Inference causal inference To infer causality, you need a randomized experiment (or a huge observational study and lots of outside information). inference to populations Generalizations
More informationPeter Hoff Minimax estimation November 12, Motivation and definition. 2 Least favorable prior 3. 3 Least favorable prior sequence 11
Contents 1 Motivation and definition 1 2 Least favorable prior 3 3 Least favorable prior sequence 11 4 Nonparametric problems 15 5 Minimax and admissibility 18 6 Superefficiency and sparsity 19 Most of
More informationAn Introduction to Probability Theory and Its Applications
An Introduction to Probability Theory and Its Applications WILLIAM FELLER (19061970) Eugene Higgins Professor of Mathematics Princeton University VOLUME II SECOND EDITION JOHN WILEY & SONS Contents I
More informationComposite Hypotheses and Generalized Likelihood Ratio Tests
Composite Hypotheses and Generalized Likelihood Ratio Tests Rebecca Willett, 06 In many real world problems, it is difficult to precisely specify probability distributions. Our models for data may involve
More informationThe optimal discovery procedure: a new approach to simultaneous significance testing
J. R. Statist. Soc. B (2007) 69, Part 3, pp. 347 368 The optimal discovery procedure: a new approach to simultaneous significance testing John D. Storey University of Washington, Seattle, USA [Received
More informationCalibration of the Empirical Likelihood Method for a Vector Mean
Calibration of the Empirical Likelihood Method for a Vector Mean Sarah C. Emerson and Art B. Owen Department of Statistics Stanford University Abstract The empirical likelihood method is a versatile approach
More informationReports of the Institute of Biostatistics
Reports of the Institute of Biostatistics No 02 / 2008 Leibniz University of Hannover Natural Sciences Faculty Title: Properties of confidence intervals for the comparison of small binomial proportions
More informationTESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION
TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION Gábor J. Székely Bowling Green State University Maria L. Rizzo Ohio University October 30, 2004 Abstract We propose a new nonparametric test for equality
More informationSTAT 135 Lab 6 Duality of Hypothesis Testing and Confidence Intervals, GLRT, Pearson χ 2 Tests and QQ plots. March 8, 2015
STAT 135 Lab 6 Duality of Hypothesis Testing and Confidence Intervals, GLRT, Pearson χ 2 Tests and QQ plots March 8, 2015 The duality between CI and hypothesis testing The duality between CI and hypothesis
More informationQUANTITATIVE TECHNIQUES
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION (For B Com. IV Semester & BBA III Semester) COMPLEMENTARY COURSE QUANTITATIVE TECHNIQUES QUESTION BANK 1. The techniques which provide the decision maker
More informationINDEX DES TRADUCTIONS ANGLAISES
STATISTIQUE THÉORIQUE ET APPLIQUÉE Tome 1 Statistique descriptive et bases de l inférence statistique Pierre Dagnelie INDEX DES TRADUCTIONS ANGLAISES Bruxelles, De Boeck, 2013, 517 p. ISBN 9782804175603
More informationTest Code: STA/STB (Short Answer Type) 2013 Junior Research Fellowship for Research Course in Statistics
Test Code: STA/STB (Short Answer Type) 2013 Junior Research Fellowship for Research Course in Statistics The candidates for the research course in Statistics will have to take two shortanswer type tests
More informationTo appear in The American Statistician vol. 61 (2007) pp
How Can the Score Test Be Inconsistent? David A Freedman ABSTRACT: The score test can be inconsistent because at the MLE under the null hypothesis the observed information matrix generates negative variance
More informationChapter 6. Hypothesis Tests Lecture 20: UMP tests and NeymanPearson lemma
Chapter 6. Hypothesis Tests Lecture 20: UMP tests and NeymanPearson lemma Theory of testing hypotheses X: a sample from a population P in P, a family of populations. Based on the observed X, we test a
More informationSTATISTICSSTAT (STAT)
StatisticsSTAT (STAT) 1 STATISTICSSTAT (STAT) Courses STAT 158 Introduction to R Programming Credit: 1 (100) Programming using the R Project for the Statistical Computing. Data objects, for loops,
More informationCHAPTER 17 CHISQUARE AND OTHER NONPARAMETRIC TESTS FROM: PAGANO, R. R. (2007)
FROM: PAGANO, R. R. (007) I. INTRODUCTION: DISTINCTION BETWEEN PARAMETRIC AND NONPARAMETRIC TESTS Statistical inference tests are often classified as to whether they are parametric or nonparametric Parameter
More informationChapter 2. Binary and Mary Hypothesis Testing 2.1 Introduction (Levy 2.1)
Chapter 2. Binary and Mary Hypothesis Testing 2.1 Introduction (Levy 2.1) Detection problems can usually be casted as binary or Mary hypothesis testing problems. Applications: This chapter: Simple hypothesis
More informationBayesian and frequentist tests of sign equality and other nonlinear inequalities
Bayesian and frequentist tests of sign equality and other nonlinear inequalities David M. Kaplan Department of Economics, University of Missouri July 14, 2015 Abstract Testing whether two parameters have
More informationPoisson Regression. Ryan Godwin. ECON University of Manitoba
Poisson Regression Ryan Godwin ECON 7010  University of Manitoba Abstract. These lecture notes introduce Maximum Likelihood Estimation (MLE) of a Poisson regression model. 1 Motivating the Poisson Regression
More informationTesting Goodness Of Fit Of The Geometric Distribution: An Application To Human Fecundability Data
Journal of Modern Applied Statistical Methods Volume 4 Issue Article 8 5 Testing Goodness Of Fit Of The Geometric Distribution: An Application To Human Fecundability Data Sudhir R. Paul University of
More informationDoseresponse modeling with bivariate binary data under model uncertainty
Doseresponse modeling with bivariate binary data under model uncertainty Bernhard Klingenberg 1 1 Department of Mathematics and Statistics, Williams College, Williamstown, MA, 01267 and Institute of Statistics,
More informationNonparametric tests, Bootstrapping
Nonparametric tests, Bootstrapping http://www.isrec.isbsib.ch/~darlene/embnet/ Hypothesis testing review 2 competing theories regarding a population parameter: NULL hypothesis H ( straw man ) ALTERNATIVEhypothesis
More information4.2 Estimation on the boundary of the parameter space
Chapter 4 Nonstandard inference As we mentioned in Chapter the the loglikelihood ratio statistic is useful in the context of statistical testing because typically it is pivotal (does not depend on any
More informationMaster s Written Examination  Solution
Master s Written Examination  Solution Spring 204 Problem Stat 40 Suppose X and X 2 have the joint pdf f X,X 2 (x, x 2 ) = 2e (x +x 2 ), 0 < x < x 2
More informationNonparametric tests. Timothy Hanson. Department of Statistics, University of South Carolina. Stat 704: Data Analysis I
1 / 16 Nonparametric tests Timothy Hanson Department of Statistics, University of South Carolina Stat 704: Data Analysis I Nonparametric one and twosample tests 2 / 16 If data do not come from a normal
More informationComment on HAC Corrections for Strongly Autocorrelated Time Series by Ulrich K. Müller
Comment on HAC Corrections for Strongly Autocorrelated ime Series by Ulrich K. Müller Yixiao Sun Department of Economics, UC San Diego May 2, 24 On the Nearlyoptimal est Müller applies the theory of optimal
More informationConsonance and the Closure Method in Multiple Testing. Institute for Empirical Research in Economics University of Zurich
Institute for Empirical Research in Economics University of Zurich Working Paper Series ISSN 14240459 Working Paper No. 446 Consonance and the Closure Method in Multiple Testing Joseph P. Romano, Azeem
More informationAdmission to the Ph.D. Programme in Statistics: 2017
Admission to the Ph.D. Programme in Statistics: 2017 Procedure: 1. The conditions for eligibility will be guided overall by the rules specified in the notification regarding Regulations for the Degree
More informationIntegral Section List for OCR Specification
Integral Section List for OCR Specification 161 Sections are listed below, covering all of AS/A level Mathematics and Further Mathematics, categorised by Module and Topic Module Topic Section Name OCR
More informationAppendix A Summary of Tasks. Appendix Table of Contents
Appendix A Summary of Tasks Appendix Table of Contents Reporting Tasks...357 ListData...357 Tables...358 Graphical Tasks...358 BarChart...358 PieChart...359 Histogram...359 BoxPlot...360 Probability Plot...360
More informationExercises Chapter 4 Statistical Hypothesis Testing
Exercises Chapter 4 Statistical Hypothesis Testing Advanced Econometrics  HEC Lausanne Christophe Hurlin University of Orléans December 5, 013 Christophe Hurlin (University of Orléans) Advanced Econometrics
More informationLecture 23: UMPU tests in exponential families
Lecture 23: UMPU tests in exponential families Continuity of the power function For a given test T, the power function β T (P) is said to be continuous in θ if and only if for any {θ j : j = 0,1,2,...}
More informationAdvanced Statistics II: Non Parametric Tests
Advanced Statistics II: Non Parametric Tests Aurélien Garivier ParisTech February 27, 2011 Outline Fitting a distribution Rank Tests for the comparison of two samples Two unrelated samples: MannWhitney
More informationStatistics for the LHC Lecture 1: Introduction
Statistics for the LHC Lecture 1: Introduction Academic Training Lectures CERN, 14 17 June, 2010 indico.cern.ch/conferencedisplay.py?confid=77830 Glen Cowan Physics Department Royal Holloway, University
More informationEstimation, Inference, and Hypothesis Testing
Chapter 2 Estimation, Inference, and Hypothesis Testing Note: The primary reference for these notes is Ch. 7 and 8 of Casella & Berger 2. This text may be challenging if new to this topic and Ch. 7 of
More informationMultilevel Statistical Models: 3 rd edition, 2003 Contents
Multilevel Statistical Models: 3 rd edition, 2003 Contents Preface Acknowledgements Notation Two and three level models. A general classification notation and diagram Glossary Chapter 1 An introduction
More informationSTAT 801: Mathematical Statistics. Hypothesis Testing
STAT 801: Mathematical Statistics Hypothesis Testing Hypothesis testing: a statistical problem where you must choose, on the basis o data X, between two alternatives. We ormalize this as the problem o
More information7 Likelihood and Maximum Likelihood Estimation
7 Likelihood and Maximum Likelihood Estimation Exercice 7.1. Let X be a random variable admitting the following probability density : x +1 I x 1 where > 0. It is in fact a particular Pareto law. Consider
More informationP Values and Nuisance Parameters
P Values and Nuisance Parameters Luc Demortier The Rockefeller University PHYSTATLHC Workshop on Statistical Issues for LHC Physics CERN, Geneva, June 27 29, 2007 Definition and interpretation of p values;
More information4 Hypothesis testing. 4.1 Types of hypothesis and types of error 4 HYPOTHESIS TESTING 49
4 HYPOTHESIS TESTING 49 4 Hypothesis testing In sections 2 and 3 we considered the problem of estimating a single parameter of interest, θ. In this section we consider the related problem of testing whether
More informationWhat s New in Econometrics? Lecture 14 Quantile Methods
What s New in Econometrics? Lecture 14 Quantile Methods Jeff Wooldridge NBER Summer Institute, 2007 1. Reminders About Means, Medians, and Quantiles 2. Some Useful Asymptotic Results 3. Quantile Regression
More informationEXACT AND ASYMPTOTICALLY ROBUST PERMUTATION TESTS. Eun Yi Chung Joseph P. Romano
EXACT AND ASYMPTOTICALLY ROBUST PERMUTATION TESTS By Eun Yi Chung Joseph P. Romano Technical Report No. 2005 May 20 Department of Statistics STANFORD UNIVERSITY Stanford, California 943054065 EXACT AND
More informationPseudoscore confidence intervals for parameters in discrete statistical models
Biometrika Advance Access published January 14, 2010 Biometrika (2009), pp. 1 8 C 2009 Biometrika Trust Printed in Great Britain doi: 10.1093/biomet/asp074 Pseudoscore confidence intervals for parameters
More informationAS and A level Further mathematics contents lists
AS and A level Further mathematics contents lists Contents Core Pure Mathematics Book 1/AS... 2 Core Pure Mathematics Book 2... 4 Further Pure Mathematics 1... 6 Further Pure Mathematics 2... 8 Further
More information388 Index Differencing test ,232 Distributed lags , 147 arithmetic lag.
INDEX Aggregation... 104 Almon lag... 135140,149 AR(1) process... 114130,240,246,324325,366,370,374 ARCH... 376379 ARlMA... 365 Asymptotically unbiased... 13,50 Autocorrelation... 113130, 142150,324325,365369
More informationDeccan Education Society s FERGUSSON COLLEGE, PUNE (AUTONOMOUS) SYLLABUS UNDER AUTONOMY. FIRST YEAR B.Sc.(Computer Science) SEMESTER I
Deccan Education Society s FERGUSSON COLLEGE, PUNE (AUTONOMOUS) SYLLABUS UNDER AUTONOMY FIRST YEAR B.Sc.(Computer Science) SEMESTER I SYLLABUS FOR F.Y.B.Sc.(Computer Science) STATISTICS Academic Year 20162017
More informationStochastic Processes. Theory for Applications. Robert G. Gallager CAMBRIDGE UNIVERSITY PRESS
Stochastic Processes Theory for Applications Robert G. Gallager CAMBRIDGE UNIVERSITY PRESS Contents Preface page xv Swgg&sfzoMj ybr zmjfr%cforj owf fmdy xix Acknowledgements xxi 1 Introduction and review
More informationA nonparametric twosample wald test of equality of variances
University of Wollongong Research Online Faculty of Informatics  Papers (Archive) Faculty of Engineering and Information Sciences 211 A nonparametric twosample wald test of equality of variances David
More information