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Fundamentals of statistical exponential families with applications in statistical decision theory. (English) Zbl 0685.62002
Institute of Mathematical Statistics Lecture Notes - Monograph Series 9. Hayward, CA: Institute of Mathematical Statistics (ISBN 0-940600-10-2). x, 283 p., open access (1986).
The monograph provides a systematic treatment of the analytic and probabilistic properties of the exponential families. Statistical applications in the area of statistical decision theory and other applications are presented. The material is covered in seven chapters with Appendix and References.
Chapter 1-3 cover basic properties, analytic properties and parametrizations. Applications including information inequality, unbiased estimates of the risk and generalized Bayes estimates are given in Chapter 4 with an Appendix on pointwise limits of Bayes procedures. Maximum likelihood estimation and duals to the maximum likelihood estimation are discussed in Chapter 5-6. Tail proabilities and complete class theorems for tests are presented in Chapter 7. The monograph provides a valuable material in statistical theory.
Reviewer: K.Alam

MSC:
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62C10 Bayesian problems; characterization of Bayes procedures
62C07 Complete class results in statistical decision theory
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Full Text: Euclid