Parametric Statistical Theory (de Gruyter Textbook)

Description

Preface Introduction Chapter 1 Sufficiency and completeness 1.1 Introduction 1.2 Sufficiency and factorization of densities 1.3 Sufficiency and exhaustivity 1.4 Minimal sufficiency 1.5 Completeness 1.6 Exponential families 1.7 Auxiliary results on families with monotone likelihood ratios 1.8 Ancillary statistics 1.9 Equivariance and invariance 1.10 Appendix: Conditional expectations, conditional distributions Chapter 2 The evaluation of estimators 2.1 Introduction 2.2 Unbiasedness of estimators 2.3 The concentration of real valued estimators 2.4 Concentration of multivariate estimators 2.5 Evaluating estimators by loss functions 2.6 The relative efficiency of estimators 2.7 Examples on the evaluation of estimators Chapter 3 Mean unbiased estimators and convex loss functions 3.1 Introduction 3.2 The Rao-Blackwell-Lehmann-Scheffé-Theorem 3.3 Examples of mean unbiased estimators with minimal convex risk 3.4 Mean unbiased estimation of probabilities 3.5 A result on bounded mean unbiased estimators Chapter 4 Testing hypotheses 4.1 Basic concepts 4.2 Critical functions, critical regions 4.3 The Neyman-Pearson Lemma 4.4 Optimal tests for composite hypotheses 4.5 Optimal tests for families with monotone likelihood ratios 4.6 Tests of Neyman structure 4.7 Most powerful similar tests for a real parameter in the presence of a nuisance parameter Chapter 5 Confidence procedures 5.1 Basic concepts 5.2 The evaluation of confidence procedures 5.3 The construction of one-sided confidence bounds and median unbiased estimators 5.4 Optimal one-sided confidence bounds and median unbiased estimators 5.5 Optimal one-sided confidence bounds and median unbiased estimators in the presence of a nuisance parameter 5.6 Examples of maximally concentrated confidence bounds Chapter 6 Consistent estimators 6.1 Introduction 6.2 A general consistency theorem 6.3 Consistency of M-estimators 6.4 Consistent solutions of estimating equations 6.5 Consistency of maximum likelihood estimators 6.6 Examples of ML estimators 6.7 Appendix: Uniform integrability, stochastic convergence and measurable selection Chapter 7 Asymptotic distributions of estimator sequences 7.1 Limit distributions 7.2 How to deal with limit distributions 7.3 Asymptotic confidence bounds 7.4 Solutions to estimating equations 7.5 The limit distribution of ML estimator sequences 7.6 Stochastic approximations to estimator sequences 7.7 Appendix: Weak convergence Chapter 8 Asymptotic bounds for the concentration of estimators and confidence bounds 8.1 Introduction 8.2 Regular sequences of confidence bounds and median unbiased estimators 8.3 Sequences of confidence bounds and median unbiased estimators with limit distributions 8.4 The convolution theorem 8.5 Maximally concentrated limit distributions 8.6 Superefficiency Chapter 9 Miscellaneous results on asymptotic distributions 9.1 Examples of ML estimators 9.2 Tolerance bounds 9.3 Probability measures with location- and scale parameters 9.4 Miscellaneous results on estimators Chapter 10 Asymptotic test theory 10.1 Introduction 10.2 Tests for a real valued functional 10.3 The asymptotic envelope power function for tests for a real valued functional References Author Index Subject Index Notation Index