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Statistics - Statistical Theory and Methods | Conditional Specification of Statistical Models

Conditional Specification of Statistical Models

Arnold, Barry C., Castillo, Enrique, Sarabia, Jose M.

1999, XVI, 416 p.

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Thisbookisanexpandedup-to-dateversionofourLectureNotesinStat- tics monograph entitled Conditionally Speci?ed Distributions. Chapters in that monograph have been edited, expanded, and brought up-to-date (1998). The concept of conditional speci?cation of distributions is not new but, except in normal families, it has not been well developed in the lite- ture. Computational di?culties undoubtedly hindered or discouraged - velopments in this direction. However, such roadblocks are of diminished importance today. Questions of compatibility of conditional and marginal speci?cations of distributions are of fundamental importance in modeling scenarios. Such issues are carefully analyzed in this book. Building on a normal conditionals model, which dates back at least to Bhattacharyya (1943), a broad spectrum of conditionally speci?ed models is developed. Models with conditionals in exponential families are particularly tractable and provide useful models in a broad variety of settings. Chapter 1 covers basic results on characterization of compatibility of conditional distributions and uniqueness of the corresponding joint dist- bution in a variety of settings. In addition, important functional equation results are presented. These prove to be basic tools in subsequent devel- ment of families of distributions with conditionals in speci?ed parametric families. Chapter 2 is focussed on the ?nite discrete case. In it, a variety of compatibility and near-compatibility results are described.

Content Level » Research

Keywords » Statistical Models

Related subjects » Statistical Theory and Methods

Table of contents 

Conditional Specification: Concepts and Theorems.- Exact and Near Compatibility in Distributions with Finite Support Sets.- Distributions with Normal Conditionals.- Conditionals in Exponential Families.- Other Conditionally Specified Families.- Improper and Nonstandard Models.- Characterizations Involving Conditional Moments.- Multivariate Extensions.- Estimation in Conditionally Specified Models.- Marginal and Conditional Specification in General.- Conditional Survival Models.- Applications to Modeling Bivariate Extremes.- Bayesian Analysis Using Conditionally Specified Models.- Conditional Specification Versus Simultaneous Equation Models.- Paella.

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