Conditionally Specified Distributions (Lecture Notes in Statistics, 73)

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

ISBN 10: 0387977945 / ISBN 13: 9780387977942

Editore: Springer, 1992

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Dati bibliografici

• Titolo: Conditionally Specified Distributions (Lecture Notes in Statistics, 73)
• Editore: Springer
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 0387977945
• ISBN 13: 9780387977942
• Rilegatura: Paperback
• Condizione: Like New
• Tipo di libro: book

Descrizione articolo

Riassunto

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.

Contenuti

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.- 4.4.1 Exponential conditionals.- 4.4.2 Normal conditionals.- 4.4.3 Gamma conditionals.- 4.4.4 Weibull conditionals.- 4.4.5 Gamma-Normal conditionals.- 4.4.6 Power-function and other weighted distributions as conditionals.- 4.4.7 Beta conditionals.- 4.4.8 Inverse Gaussian conditionals.- 4.4.9 Three discrete examples (binomial, geometric and Poisson).- 5 Other conditionally specified families.- 5.1 Introduction.- 5.2 Bivariate Distributions with Pareto conditionals.- 5.3 Some extensions of the Pareto case.- 5.3.1 Pearson type VI distributions.- 5.3.2 Burr type XII distributions.- 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 Conditionals in 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.