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Statistical Theory and Inference

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概要 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 err...or, 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.続きを見る
目次 Probability and Expectations.- Multivariate Distributions
Exponential Families.- Sufficient Statistics.- Point Estimation I.-Point Estimation II
Testing Statistical Hypotheses.- Large Sample Theory.- Confidence Intervals.- Some Useful Distributions
Bayesian Methods
Stuff for Students.
本文を見る Full text available from Springer Mathematics and Statistics eBooks 2014 English/International

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登録日 2020.06.27
更新日 2020.06.28