In this paper, a new measure of dependence is proposed. Our approach is based on transforming univariate data to the space where the marginal distributions are normally distributed and then, using the inverse transformation to obtain the distribution function in the original space. The...

In the present paper, we propose an exact test on the structure of the covariance matrix. In its development the properties of the Wishart distribution are used. Unlike the classical likelihood-ratio type tests and the tests based on the empirical distance, whose statistics depend on the total...

In this paper we consider the distribution of the product of a Wishart random matrix and a Gaussian random vector. We derive a stochastic representation for the elements of the product. Using this result, the exact joint density for an arbitrary linear combination of the elements of the product...

In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The...

In this paper we discuss the distributions and independency properties of several generalizations of the Wishart distribution. First, an analog to Muirhead [R.J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982] Theorem 3.2.10 for the partitioned matrix is...