Dependence Orderings and Their Applications

Subhash Kochar

Suppose we have two bivariate random vectors and we want to compare them according to the degree of dependence between their component random variables. Rather than using a single summary statistic like coefficient of correlation, it is more useful and informative to compare the whole distributions or some aspects of them. For this purpose, several partial orders have been introduced in the literature assuming that their marginal distributions are identical. But in many problems of practical interest, this is not the case. It will be discussed as how to modify the existing partial orders to overcome this difficulty. The modified partial orders for dependence are copula based. Applications of these orders to compare dependence between pairs of order statistics, record values and generalized order statistics will be discussed.

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