Joe H. Multivariate Models and Dependence Concepts

Springer, 1997. — 416.This book is devoted to (a) multivariate models for non-normal response, an area of probability and statistics with increasing activity and applications, and (b) dependence concepts that are useful for analysing properties of multivariate models. It also adds to the knowledge of the space of multivariate distributions.
The methods and models of this book extend commonly used univariate models to multivariate models in which parameters of the models can be considered as univariate parameters or dependence parameters, and allow one to make a variety of inferences as well as assess assumptions, do diagnostic checks, make model comparisons and perform sensitivity analyses. These are not all possible with the method of generalized estimating equations (GEEs), which is based on partly specified probability models. There have been many advances in research in multivariate non-normal distributions since researchers proposed methods like the GEE approach partly because of a lack of existing models. The models and methods here are more general and more flexible, and less dependent on assumptions, than are GEEs.Basic concepts of dependence
Fréchet classes
Construction of multivariate distributions
Parametric families of copulas
Multivariate extreme value distributions
Multivariate discrete distributions
Multivariate models with serial dependence 24
Models from given conditional distributions
Statistical inference and computation
Data analysis and comparison of models