Conditionally Specified Distributions - Barry C. Arnold

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Biographie:
Carlos A. Coelho is a Full Professor at the Mathematics Department of Nova University of Lisbon, Portugal. He obtained his Ph.D. in Biostatistics from the University of Michigan, USA. An Elected Member of the International Statistical Institute, he is primarily pursuing research in the fields of mathematical statistics and distribution theory, e.g. exact and near-exact distributions for likelihood ratio statistics used in multivariate analysis. Barry C. Arnold is a Distinguished Professor in the Department of Statistics at the University of California, Riverside, USA. He holds a Ph.D. in Statistics from Stanford University. He is a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics and a former Elected Member of the International Statistical Institute. His research interests include multivariate models, inequality measurement and ordered data....

Sommaire:
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.