Topics in Statistical Dependence (Lecture Notes-Monograph Series) - ISBN:0940600234

Topics in Statistical Dependence (Lecture Notes-Monograph Series)

Date: 09 April 2011, 14:06

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Concepts of positive dependence are becoming increasingly important in probability, statistics and their applications. While these concepts are traditionally viewed as focusing on positive and negative dependence for random vectors, they also are related to broader issues in the modeling and the analysis of multivariate data, and, in particular, ordinal data.
Historically, positive dependence for the multivariate normal distribution had been synonymous with positive correlations. Other subsequently developed multivariate distributions were often interpreted with this perspective. It was
eventually realized that positive correlations can have substantially different meanings for other multivariate distributions than they have for the multivariate normal.
In fact, it has been more recently demonstrated that several different important positive dependence concepts which are equivalent for multivariate normal distributions are not equivalent, in general, for multivariate distributions. In particular the concept of association is stronger than positive orthant dependence which is stronger than positive correlations. Thus, in a certain sense, many of the positive dependence concepts discussed or referenced in this volume, are outgrowths of original attempts to nonparametrically capture and extend certain properties of the multivariate normal. Additionally, other types of dependence came about from extending certain univariate properties, such as the memoryless property of the exponential distribution.

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