Fundamentals of statistical exponential families: with applications in statistical decision theory / Lawrence D. Brown

Auteur: Brown, Lawrence David (1940-2018) - AuteurType de document: Livre numériqueCollection: Lecture notes-monograph series ; 9Langue: anglaisÉditeur: Hayward, CA : Institute of Mathematical Statistics, 1986 ISBN: 0940600102 Note: 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. (Zentralblatt) Sujets MSC: 62-02 Statistics -- Research exposition (monographs, survey articles)
62C10 Statistics -- Decision theory -- Bayesian problems; characterization of Bayes procedures
62C07 Statistics -- Decision theory -- Complete class results
62E10 Statistics -- Distribution theory -- Characterization and structure theory
En-ligne: OA - accès libre | MathSciNet

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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. (Zentralblatt)

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