A Course in Mathematical Statistics and Large Sample Theory

Description

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. Front Matter....Pages i-xi Front Matter....Pages 1-1 Introduction....Pages 3-9 Decision Theory....Pages 11-17 Introduction to General Methods of Estimation....Pages 19-37 Sufficient Statistics, Exponential Families, and Estimation....Pages 39-65 Testing Hypotheses....Pages 67-113 Front Matter....Pages 115-115 Consistency and Asymptotic Distributions of Statistics....Pages 117-164 Large Sample Theory of Estimation in Parametric Models....Pages 165-201 Tests in Parametric and Nonparametric Models....Pages 203-256 The Nonparametric Bootstrap....Pages 257-265 Nonparametric Curve Estimation....Pages 267-278 Front Matter....Pages 279-279 Edgeworth Expansions and the Bootstrap....Pages 281-302 Fréchet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces....Pages 303-315 Multiple Testing and the False Discovery Rate....Pages 317-323 Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory....Pages 325-332 Miscellaneous Topics....Pages 333-341 Back Matter....Pages 343-389