Conditionally Specified Distributions - Arnold, Barry C.

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.