Ebook: Conditionally Specified Distributions

The concept of conditional specification is not new. It is likely that earlier investigators in this area were deterred by computational difficulties encountered in the analysis of data following con­ ditionally specified models. Readily available computing power has swept away that roadblock. A broad spectrum of new flexible models may now be added to the researcher's tool box. This mono­ graph provides a preliminary guide to these models. Further development of inferential techniques, especially those involving concomitant variables, is clearly called for. We are grateful for invaluable assistance in the preparation of this monograph. In Riverside, Carole Arnold made needed changes in grammer and punctuation and Peggy Franklin miraculously transformed minute hieroglyphics into immaculate typescript. In Santander, Agustin Manrique ex­ pertly transformed rough sketches into clear diagrams. Finally, we thank the University of Cantabria for financial support which made possible Barry C. Arnold's enjoyable and productive visit to S- tander during the initial stages of the project. Barry C. Arnold Riverside, California USA Enrique Castillo Jose Maria Sarabia Santander, Cantabria Spain January, 1991 Contents 1 Conditional Specification 1 1.1 Why? ............. ........ . 1 1.2 How may one specify a bivariate distribution? 2 1.3 Early work on conditional specification 4 1.4 Organization of this monograph . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5 2 Basic Theorems 7 Compatible conditionals: The finite discrete case.

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The focus of this monograph is the study of general classes of conditionally specified distributions. Until recently, the analysis of data using conditionally specified models was regarded as computationally difficult, but the advent of readily available computing power has re-invigorated interest in this topic. The authors' aim is to present a guide to conditionally specified models and to consider estimation and simulation methods for such models. The book begins by surveying joint distributions in a variety of settings and presenting results on functional equations which are used throughout the text. Subsequent chapters cover a wide variety of families of conditional distributions, extensions to multivariate situations, and the application to estimation techniques (both classical and Bayesian) and simulation techniques.

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The focus of this monograph is the study of general classes of conditionally specified distributions. Until recently, the analysis of data using conditionally specified models was regarded as computationally difficult, but the advent of readily available computing power has re-invigorated interest in this topic. The authors' aim is to present a guide to conditionally specified models and to consider estimation and simulation methods for such models. The book begins by surveying joint distributions in a variety of settings and presenting results on functional equations which are used throughout the text. Subsequent chapters cover a wide variety of families of conditional distributions, extensions to multivariate situations, and the application to estimation techniques (both classical and Bayesian) and simulation techniques.
Content:
Front Matter....Pages i-xii
Conditional Specification....Pages 1-6
Basic Theorems....Pages 7-19
Distributions with normal conditionals....Pages 20-34
Conditionals in Exponential Families....Pages 35-54
Other conditionally specified families....Pages 55-76
Impossible Models....Pages 77-86
Characterizations involving conditional moments....Pages 87-96
Multivariate extensions....Pages 97-108
Parameter estimation in conditionally specified models....Pages 109-129
Simulations....Pages 130-136
Bibliographic Notes....Pages 137-140
Back Matter....Pages 141-155

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The focus of this monograph is the study of general classes of conditionally specified distributions. Until recently, the analysis of data using conditionally specified models was regarded as computationally difficult, but the advent of readily available computing power has re-invigorated interest in this topic. The authors' aim is to present a guide to conditionally specified models and to consider estimation and simulation methods for such models. The book begins by surveying joint distributions in a variety of settings and presenting results on functional equations which are used throughout the text. Subsequent chapters cover a wide variety of families of conditional distributions, extensions to multivariate situations, and the application to estimation techniques (both classical and Bayesian) and simulation techniques.
Content:
Front Matter....Pages i-xii
Conditional Specification....Pages 1-6
Basic Theorems....Pages 7-19
Distributions with normal conditionals....Pages 20-34
Conditionals in Exponential Families....Pages 35-54
Other conditionally specified families....Pages 55-76
Impossible Models....Pages 77-86
Characterizations involving conditional moments....Pages 87-96
Multivariate extensions....Pages 97-108
Parameter estimation in conditionally specified models....Pages 109-129
Simulations....Pages 130-136
Bibliographic Notes....Pages 137-140
Back Matter....Pages 141-155
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