Cover

Series-title

Title

Copyright

Dedication

Contents

Preface

1 Motivation and Basic Tools

1.1 Introduction

1.2 Illustrative Examples and Motivation

1.3 Synthesis of Finite to Asymptotic Statistical Methods

1.4 The Organization of the Book

1.5 Basic Tools and Concepts

1.6 Exercises

2 Estimation Theory

2.1 Introduction

2.2 Basic Concepts

2.3 Likelihood, Information, and Sufficiency

2.4 Methods of Estimation

2.5 Finite Sample Optimality Perspectives

2.6 Concluding Notes

2.7 Exercises

3 Hypothesis Testing

3.1 Introduction

3.2 The Neyman-Pearson Paradigm

3.3 Composite Hypotheses: Beyond the Neyman-Pearson Paradigm

3.4 Invariant Tests

3.5 Concluding Notes

3.6 Exercises

4 Elements of Statistical Decision Theory

4.1 Introduction

4.2 Basic Concepts

4.3 Bayes Estimation Methods

4.4 Bayes Hypothesis Testing

4.5 Confidence Sets

4.6 Concluding Notes

4.7 Exercises

5 Stochastic Processes: An Overview

5.1 Introduction

5.2 Processes with Markov Dependencies

5.3 Discrete Time-Parameter Processes

5.4 Continuous Time-Parameter Processes

5.5 Exercises

6 Stochastic Convergence and Probability Inequalities

6.1 Introduction

6.2 Modes of Stochastic Convergence

6.3 Probability Inequalities and Laws of Large Numbers

6.4 Extensions to Dependent Variables

6.5 Miscellaneous Convergence Results

6.6 Concluding Notes

6.7 Exercises

7 Asymptotic Distributions

7.1 Introduction

7.2 Some Important Tools

7.3 Central Limit Theorems

7.4 Rates of Convergence to Normality

7.5 Projections and Variance-Stabilizing Transformations

7.6 Quadratic Forms

7.7 Order Statistics and Empirical Distributions

7.8 Concluding Notes

7.9 Exercises

8 Asymptotic Behavior of Estimators and Tests

8.1 Introduction

8.2 Estimating Equations and Local Asymptotic Linearity

8.3 Asymptotics for MLE

8.4 Asymptotics for Other Classes of Estimators

8.5 Asymptotic Efficiency of Estimators

8.6 Asymptotic Behavior of Some Test Statistics

8.7 Resampling Methods

8.8 Concluding Remarks

8.9 Exercises

9 Categorical Data Models

9.1 Introduction

9.2 Nonparametric Goodness-of-Fit Tests

9.3 Estimation and Goodness-of-Fit Tests: Parametric Case

9.4 Some Other Important Statistics

9.5 Concluding Notes

9.6 Exercises

10 Regression Models

10.1 Introduction

10.2 Generalized Least-Squares Procedures

10.3 Robust Estimators

10.4 Nonlinear Regression Models

10.5 Generalized Linear Models

10.6 Generalized Least-Squares Versus Generalized Estimating Equations

10.7 Nonparametric Regression

10.8 Concluding Notes

10.9 Exercises

11 Weak Convergence and Gaussian Processes

11.1 Introduction

11.2 Weak Invariance Principles

11.3 Weak Convergence of Partial Sum Processes

11.4 Weak Convergence of Empirical Processes

11.5 Weak Convergence and Statistical Functionals

11.6 Weak Convergence and Nonparametrics

11.7 Strong Invariance Principles

11.8 Concluding Notes

11.9 Exercises

Bibliography

Index