Statistical Theory and Inference

✍ Scribed by David J. Olive (auth.)

Publisher: Springer International Publishing
Year: 2014
Tongue: English
Leaves: 438
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families.

Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.

✦ Table of Contents

Front Matter....Pages i-xii
Probability and Expectations....Pages 1-27
Multivariate Distributions and Transformations....Pages 29-79
Exponential Families....Pages 81-99
Sufficient Statistics....Pages 101-128
Point Estimation I....Pages 129-155
Point Estimation II....Pages 157-182
Testing Statistical Hypotheses....Pages 183-213
Large Sample Theory....Pages 215-256
Confidence Intervals....Pages 257-290
Some Useful Distributions....Pages 291-357
Bayesian Methods....Pages 359-371
Stuff for Students....Pages 373-413
Back Matter....Pages 415-434

✦ Subjects

Statistical Theory and Methods; Probability Theory and Stochastic Processes; Statistics, general

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