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Statistics - Statistical Theory and Methods | Statistical Theory and Inference

Statistical Theory and Inference

Olive, David

2014, XII, 434 p. 8 illus.

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  • Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory
  • Many homework problems with over 30 pages of solutions
  • Covers complete sufficient statistics, maximum likelihood estimation, uniformly minimum unbiased estimators, UMP tests, and large sample theory

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.

Content Level » Graduate

Keywords » exponential familes - large sample theory - point estimators - statistical inference - statistical theory

Related subjects » Probability Theory and Stochastic Processes - Statistical Theory and Methods - Statistics

Table of contents 

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.

Distribution rights 

Distribution rights for India: Researchco Book Centre, New Delhi, India

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