A Course in Mathematical Statistics and Large Sample Theory

✍ Scribed by Bhattacharya, Rabindra Nath; Lin, Lizhen; Patrangenaru, Victor

• Publisher: Springer
• Year: 2016
• Tongue: English
• Leaves: 386
• Series: Springer Texts in Statistics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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

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

✦ Subjects

Mathematical statistics;Sampling (Statistics);Statistique mathématique;Échantillonnage (statistique)