A Course in Mathematical Statistics and Large Sample Theory (Springer Texts in Statistics)

by Rabi Bhattacharya (Author), Lizhen Lin (Author), Victor Patrangenaru (Author)



Large Sample Theory with many worked examples, numerical calculations, and simulations to illustrate theory

Appendices provide ready access to a number of standard results, with many proofs

Solutions given to a number of selected exercises from Part I

Part II exercises with a certain level of difficulty appear with detailed hints

This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics.
Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

Table of contents (15 chapters)

Introduction

Decision Theory

Introduction to General Methods of Estimation

Sufficient Statistics, Exponential Families, and Estimation

Testing Hypotheses

Consistency and Asymptotic Distributions of Statistics

Large Sample Theory of Estimation in Parametric Models

Tests in Parametric and Nonparametric Models

The Nonparametric Bootstrap

Nonparametric Curve Estimation

Edgeworth Expansions and the Bootstrap

Fréchet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces

Multiple Testing and the False Discovery Rate

Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory

Miscellaneous Topics