Abstract:

The paper is devoted to extension of results obtained in paper ［1］to mul tivariate t distributions case. It is shown that the divergence between two mul tivariate t distributions closely depends on the maximum eigenvalue of the rati o of scale matrices in the distributions. As an application, a kind of e ntropy loss function in estimating the unknown positive definite matrix is establis hed.

Key words: Multivariatet distribution, Kullback Leibler divergence, Entropy loss function