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.

Autorentext

Albert W. Marshall is Professor Emeritus of Statistics at the University of British Columbia. His fundamental contributions to reliability theory have had a profound effect in furthering its development. Ingram Olkin is Professor Emeritus of Statistics at Stanford University. He has made fundamental contributions in multivariate analysis, and in the development of statistical methods in meta-analysis, which have resulted in its use in many applications. Barry C. Arnold is Distinguished Professor of Statistics at the University of California, Riverside. His previous books deal with Pareto Distributions, Order Statistics, Record Values, Conditionally Specified Distributions, and the Lorenz Order.

Klappentext

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.

Inhalt
1 Conditional Specification.- 1.1 Why?.- 1.2 How may one specify a bivariate distribution?.- 1.3 Early work on conditional specification.- 1.4 Organization of this monograph.- 2 Basic Theorems.- 2.1 Compatible conditionals: The finite discrete case.- 2.2Compatibility in more general settings.- 2.3Uniqueness.- 2.4 Conditionals in prescribed families.- 2.5 An example.- 3 Distributions with normal conditionals.- 3.1 Variations on the classical bivariate normal theme.- 3.2 Normal conditionals.- 3.3 Properties of the normal conditionals distribution.- 3.4 The centered model.- 4 Conditionals in Exponential Families.- 4.1 Introduction.- 4.2 Distributions with conditionals in given exponential families.- 4.3 Dependence in CEF distributions.- 4.4 Examples.- 5 Other conditionally specified families.- 5.1 Introduction.- 5.2 Bivariate Distributions with Pareto conditionals.- 5.3 Some extensions of the Pareto case.- 5.4 Bivariate distributions with Cauchy conditionals.- 5.5 Bivariate distributions with uniform conditionals.- 5.6 Possibly translated exponential conditionals.- 5.7 Bivariate distributions with scaled beta conditionals.- 5.8 Weibull and logistic conditionals.- 5.9 Mixtures.- 6 Impossible Models.- 6.1 Introduction.- 6.2 Logistic Regression.- 6.3 Uniform conditionals.- 6.4 Exponential and Weibull conditionals.- 6.5 Measurement error models.- 6.6 Stochastic processes and Wohler fields.- 6.6.1 The Gumbel-Gumbel model.- 6.6.2 The Wei bull-Weibull model.- 7 Characterizations involving conditional moments.- 7.1 Introduction.- 7.2 Mardia's bivariate Pareto distribution.- 7.3Linear regressions with conditionals in exponential families.- 7.4Linear regressions with conditionals in location families.- 7.5Specified regressions with conditionals in scale families.- 7.6 Conditionalsin location-scale families with specified moments.- 8 Multivariate extensions.- 8.1 Extension by underlining.- 8.2 Compatibility in 3 dimensions.- 8.3 Conditionals in prescribed families.- 8.4 Conditionals in exponential families.- 8.5 Examples.- 8.6 Further extension by underlining.- 9 Parameter estimation in conditionally specified models.- 9.1 The ubiquitous norming constant.- 9.2 Maximum likelihood.- 9.3 Pseudolikelihood involving conditional densities.- 9.4 Marginal likelihood.- 9.5 An efficiency comparison.- 9.6 Method of moments estimates.- 9.7 Bayesian estimates.- 10 Simulations.- 10.1 Introduction.- 10.2 The rejection method.- 10.3 Application to models with conditionals in exponential families.- 10.4 Other conditionally specified models.- 10.5 A direct approach not involving rejection.- 11 Bibliographic Notes.- 11.1 Introduction.- 11.2 Basic theorems.- 11.3 Distributions with normal conditionals.- 11.4 Conditionals in exponential families.- 11.5 Other conditionally specified Families.- 11.6 Impossible models.- 11.7 Characterizations involving conditional moments.- 11.8 Multivariate extensions.- 11.9 Parameter estimation in conditionally specified models.- 11.10 Simulations.