On Multivariate Measures Of Association For Dependent Risks

In light of complexity of correlations between random variables(especially multidimensional random variables) in probability theory and statistics,it is invariably postulated that random variables are independent from one another.Nevertheless,in practice absolute independence is hard to be satisfied.Moreover,the conclusion we reach,after ignoring dependence of random variables,can not conform to the fact. The paper improves the measurement which depict the concordance from the dependence among the random variables,on the basis of the previous studies,wc give the extensions to the multivariate measures(i.e.Kendall'sΥ,Spearman'sρ,Blomqvist'sβ,Gini's(?)) of association that base on the concept of multi-concordance between two random vectors and discuss the relationship between different dimension's measures of association.The structure of the paper is as follows.In chapter 1,we present the background of the paper and simply introduce the main rescarch;In chapter 2,we introduce basic definitions and properties used in the sequel;In chapter 3,we give the definition of multi-concordance and provide extensions of Kendall'sΥ,Spearman'sρ,Blomqvist'sβ,Gini'sγbased on multi-concordance.In chapter 4,we study applications of multi-dimensional measures of association and some examples.