Distributions With Given Marginals and Statistical Modelling

Editors: Carles M. Cuadras, Josep Fortiana, José A. Rodriguez-Lallena



This volume contains the papers presented at the meeting "Distributions with given marginals and statistical modelling," held in Barcelona (Spain), July 17- 20, 2000. This is the fourth meeting on given marginals, showing that this topic has aremarkable interest. BRIEF HISTORY The construction of distributions with given marginals started with the seminal papers by Hoeffding (1940) and Fn!chet (1951). Since then, many others have contributed on this topic: Dall' Aglio, Farlie, Gumbel, Johnson, Kellerer, Kotz, Morgenstern, Marshali, Olkin, Strassen, Vitale, Whitt, etc., as weIl as Arnold, Cambanis, Deheuvels, Genest, Frank, Joe, Kirneldorf, Nelsen, Ruschendorf, Sampson, Scarsini, Tiit, etc. In 1957 Sklar and Schweizer introduced probabilistic metric spaces. In 1975 Kirneldorf and Sampson studied the uniform representation of a bivariate dis tribution and proposed the desirable conditions that should be satisfied by any bivariate family. In 1991 Darsow, Nguyen and Olsen defined a natural operation between cop ulas, with applications in stochastic processes. In 1993, AIsina, Nelsen and Schweizer introduced the notion of quasi-copula.

Table of contents (24 chapters)

Front Matter

On Quasi-Copulas and Metrics

Multivariate Survival Models Incorporating Hidden Truncation

Variation Independent Parameterizations of Multivariate Categorical Distributions

A New Proof of Sklar’s Theorem

Diagonal Distributions Via Orthogonal Expansions and Tests of Independence

Principal Components of the Pareto Distribution

Shape of a Distribution Through the L2-Wasserstein Distance

Realizable Monotonicity and Inverse Probability Transform

An Ordering Among Generalized Closeness Criteria

The Bertino Family of Copulas

Time Series Models with Given Interactions

Conditions for the Asymptotic Semiparametric Efficiency of an Omnibus Estimator of Dependence Parameters in Copula Models

Maximum Correlations and Tests of Goodness-of-Fit

Which is the Right Laplace?

A New Grade Measure of Monotone Multivariate Separability

Some Integration-by-Parts Formulas Involving 2-Copulas

Bayesian Robustness for Multivariate Problems

Concordance and Copulas: A Survey

Multivariate Archimedean Quasi-Copulas

Some New Properties of Quasi-Copulas

Assignment Models for Constrained Marginals and Restricted Markets

Variance Minimization and Random Variables with Constant Sum

Conditional Expectations and Idempotent Copulæ

Existence of Multivariate Distributions with Given Marginals

Back Matter