Statistical Theory and Inference

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.

• exponential familes
• large sample theory
• point estimators
• statistical inference
• statistical theory

“This book describes the most important aspects of subjective classical statistical theory and inference similar to the treatment in Rohatgi … . The book can be considered as a guide for teachers and students in the first or second courses in classical statistical methods … . The book has been written with careful details and can serve as a good reference on the topics it covers. It is highly recommended … .” (Mariano Ruiz Espejo, International Statistical Review, Vol. 83 (1), 2015)

“This is a textbook for a one semester graduate course in statistical theory and covers mainly parametric methods. Its presentation based on the theory of exponential families (EFs) and the concept of support of the distribution makes the topics much more accessible to students.” (Oleksandr Kukush, zbMATH, Vol. 1305, 2015)

• Department of Mathematics, Southern Illinois University, Carbondale, USA

  David J. Olive

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