Conditional specification of statistical models. Exp. up-to-date version of 1992 ed. (English) Zbl 0932.62001

Arnold, Barry C.; Castillo, Enrique; Sarabia, José María

Springer Series in Statistics. New York, NY: Springer. xvi, 411 p. DM 149.00; öS 1088.00; sFr 136.00; £51.50; $ 74.95 (1999).

This book is an expanded up-to-date version of our Lecture Notes in Statistics monograph from 1992, entiteled “Conditionally specified distributions”, see the review Zbl 0749.62002. Chapters in that monograph have been edited, expanded and brought up-to-date.
The concept of conditional specification of distributions is not new but, except in normal families, it has not been well developed in the literature. Computational difficulties undoubtedly hindered or discouraged developments in this direction. However, such roadblocks are of diminished importance today. Questions of compatibility of conditional and marginal specifications of distributions are of fundamental importance in modeling scenarios. Such issues are carefully analyzed in this book. Building on a normal conditionals model, a broad spectrum of conditionally specified models is developed. Models with conditionals in exponential families are particularly tractable and provide useful models in a broad variety of settings.

MSC:

62-02	Research exposition (monographs, survey articles) pertaining to statistics
62E10	Characterization and structure theory of statistical distributions
62H05	Characterization and structure theory for multivariate probability distributions; copulas

Keywords:

exact compatibility; near compatibility; normal conditionals; exponential families; improper models; nonstandard models; characterizations; multivariate extensions; estimation; marginal specification; survival models; bivariate extremes; Bayesian analysis; simultaneous equation models; simulation

Citations:

Zbl 0749.62002