Dependence And Dependence Measures Between Random Vectors

In this paper, we mainly study the dependence and dependence measures between random vectors.We propose a dependence function D and dependence measuresρv+,ρv-between random vectors and give the properties of them respectively. A further version ofρv- is given under the condition that the joint copula is absolutely continuous.A measure of tail dependence between random vectors is derived from the function D.To solve the prob-lem that the upper and lower bounds ofρv-,ρv+ can not reach 1 and-1,we propose a new dependence measure q between random vectors.Some examples are given to demonstrate the importance of the theory proposed.Applying Archimedean copula to the dependence between random vectors,we obtain some further conclusions.For normal vectors, the up-per and lower bounds ofΤn andρn are given in the form of the linear correlation coefficient.