Lower Bounds for Minimum Covariance Matrices in Time Series Regression Problems

Lower bounds for Minimum Interference Frequency Assignment Problems

In this paper we describe a new lower bound procedure for the minimum interference frequency assignment problem (MI-FAP). In the MI-FAP we have to assign frequencies to transmitter-receiver pairs in such a way that the cumulative interference in the communication network is minimized. Mainly due to the fairly large number of available frequencies, exact methods fail to solve the more di cult in...

Eigenvalue variance bounds for covariance matrices

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for Wigner matrices [7] and stated the results for covariance matrices. They are proved in the present paper. Relying on the LUE example, which needs to be investi...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Structured covariance matrices in multivariate regression models

A similarity matrix is a covariance matrix generated by additive nested common factors having independent components. The set of such matrices is a structured subset of covariance matrices, closed under permutation and restriction, which makes it potentially useful as a sub-model for the joint dependence of several responses. It is also equal to the set of rooted trees. Some issues connected wi...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...