Theoretical Statistics and Mathematics Unit, ISI Delhi

November 2, 2011 (Wednesday) ,
3:30 PM at Webinar

Speaker:
S. C. Kochar,
Portland State University

Title:
Dependence comparisons and their applications

Abstract of Talk

Suppose we want to compare the degree of dependence between the components of two bivariate random vectors. Rather than using a single summary statistic such as coefficient of correlation, it is more useful and informative to compare the whole distributions or some aspects of them. For this purpose, various 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 over come this difficulty. The modified partial orders for dependence are copula based. Applications of these orders to compare the degree of dependence between pairs of order statistics, record values and generalized order statistics will be discussed. We also consider the case when the random variables are independent but not identically distributed. Explicit expressions are obtained for the population value of Kendall's coefficient of concordance between any two order statistics as well as record values of a random sample.