A Course in Mathematical Statistics and Large Sample Theory

• Main Authors: Bhattacharya, Rabi (Author), Lin, Lizhen (Author), Patrangenaru, Victor (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2016.
• Series: Springer Texts in Statistics,
• Subjects: Statistics.; Mathematical statistics.; Biostatistics.; Probabilities.; Statistical Theory and Methods.; Probability and Statistics in Computer Science.; Statistics for Business/Economics/Mathematical Finance/Insurance.; Probability Theory and Stochastic Processes.; Statistics and Computing/Statistics Programs.

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 present...

Table of Contents:

• 1 Introduction
• 2 Decision Theory
• 3 Introduction to General Methods of Estimation
• 4 Sufficient Statistics, Exponential Families, and Estimation
• 5 Testing Hypotheses
• 6 Consistency and Asymptotic Distributions and Statistics
• 7 Large Sample Theory of Estimation in Parametric Models
• 8 Tests in Parametric and Nonparametric Models
• 9 The Nonparametric Bootstrap
• 10 Nonparametric Curve Estimation
• 11 Edgeworth Expansions and the Bootstrap
• 12 Frechet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces
• 13 Multiple Testing and the False Discovery Rate
• 14 Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory
• 15 Miscellaneous Topics
• Appendices
• Solutions of Selected Exercises in Part 1.