Theoretical Statistics Topics for a Core Course /

• Main Author: Keener, Robert W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Series: Springer Texts in Statistics,
• Subjects: Statistics.; Mathematical statistics.; Statistical Theory and Methods.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-93839-4

Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the n...

Table of Contents:

• Probability and measure
• Exponential families
• Risk, sufficiency, completeness, and ancillarity
• Unbiased estimation
• Curved exponential families
• Conditional distributions
• Bayesian estimation
• Large sample theory
• Estimating equations and maximum likelihood
• Equivariant estimation
• Empirical bayes and shrinkage estimators
• Hypothesis testing
• Optimal tests in higher dimensions
• General linear model
• Bayesian inference: Modeling and computation
• Asymptotic optimality
• Large sample theory for likelihood ratio tests
• Nonparametric regression
• Bootstrap methods
• Sequential methods.