Dependence Measures Between Random Vectors On The Copulas And Related Statistics

In this paper, we mainly consider the construction, the statistical inference and the application of the measure of dependence of random vectors which is based on the copula. The dependence plays a key role in statistics. Copula functions represent a methodology which has recently become the most significant new tool to handle the dependence. We use the combination of copula functions to construct the measure of dependence between random vectors. Using this method, we can deal with the shortcoming of the other mea-sure of dependence. Numerical measures and functional measures based on Copula are proposed, and therefore invariant with respect to strictly increasing transformations of random vectors. In the bivariate case, numerical measures coincide with the population version of Spearman’s p. Functional measures can be used in the study of dependence between vectors and both tail monotonicity and quadrant dependence are properties of the functional measures. For these measures, nonparametric estimators are introduced via the empirical Copula and large sample properties of them will be discussed.