In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$. The precision matrix is...

In this paper, we introduce a new class of elliptically contoured processes. The suggested process possesses both the generality of the conditional heteroscedastic autoregressive process and the elliptical symmetry of the elliptically contoured distributions. In the empirical study we find the...

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 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 derive the Stein-Haff identity for the multivariate elliptically contoured matrix distributions. Our results generalize the results of the papers by [Stein, C., 1977. Personal communication. Unpublished notes on estimating the covariance matrix] and [Haff, L.R., 1979a. An...

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 this paper, we propose a nonparametric method based on jackknife empirical likelihood ratio to test the equality of two variances. The asymptotic distribution of the test statistic has been shown to follow χ-super-2 distribution with the degree of freedom 1. Simulations have been conducted...

For a class of skew-normal matrix distributions, the density function, moment generating function and independence conditions are obtained. The noncentral skew Wishart distribution is defined, and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart...

Marshall and Olkin (1997)  [14] provided a general method to introduce a parameter into a family of distributions and discussed in details about the exponential and Weibull families. They have also briefly introduced the bivariate extension, although not any properties or inferential issues...

The gamma and beta functions have been generalized in several ways. The multivariate beta and multivariate gamma functions due to Ingham and Siegel have been defined as integrals having the integrand as a scalar function of the real symmetric matrix. In this article, we define extended matrix...