We consider the asymptotic joint distribution of the eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues become infinitely dispersed. We show that the normalized sample eigenvalues and the relevant elements of the sample eigenvectors are asymptotically all mutually...

For orthogonally invariant estimation of [Sigma] of Wishart distribution using Stein's loss, any estimator which does not preserve the order of the sample eigenvalues is dominated by a modified estimator preserving the order.

This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately normalized eigenvectors and eigenvalues asymptotically...

An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss.

Modified estimators for the contribution rates of population eigenvalues are given under an elliptically contoured distribution. These estimators decrease the bias of the classical estimator, i.e. the sample contribution rates. The improvement of the modified estimators over the classical...

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 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...