On Minimax Detection of Gaussian Stochastic Sequences with Imprecisely Known Means and Covariance Matrices

On Detection of Gaussian Stochastic Sequences

The problem of minimax detection of Gaussian random signal vector in White Gaussian additive noise is considered. It is supposed that an unknown vector $\boldsymbol{\sigma}$ of the signal vector intensities belong to the given set ${\mathcal E}$. It is investigated when it is possible to replace the set ${\mathcal E}$ by a smaller set ${\mathcal E}_{0}$ without loss of quality (and, in particul...

Minimax Estimation of Large Covariance Matrices 1369

Sharp minimax tests for large covariance matrices

We consider the detection problem of correlations in a p-dimensional Gaussian vector for p large, when we observe n independent, identically distributed random vectors. We assume that the covariance matrix vary in some ellipsoid with parameter α > 1/2 and total energy bounded by L > 0. We prove here both rate and sharp asymptotic results in the minimax setup. Our test procedure is a U-statistic...

Minimax optimal estimation of general bandable covariance matrices

Cai et al. (2010) [4] have studied the minimax optimal estimation of a collection of large bandable covariance matrices whose off-diagonal entries decay to zero at a polynomial rate. They have shown that the minimax optimal procedures are fundamentally different under Frobenius and spectral norms, regardless of the rate of polynomial decay. To gain more insight into this interesting problem, we...

Minimax Estimation of Large Covariance Matrices under l1-Norm

Driven by a wide range of applications in high-dimensional data analysis, there has been significant recent interest in the estimation of large covariance matrices. In this paper, we consider optimal estimation of a covariance matrix as well as its inverse over several commonly used parameter spaces under the matrix l1 norm. Both minimax lower and upper bounds are derived. The lower bounds are ...