We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by minimizing the quadratic loss function and joint penalty of `1 norm and variance of its eigenvalues. In contrast to some of the existing methods of covariance...

There is a growing need for the ability to specify and generate correlated random variables as primitive inputs to stochastic models. Motivated by this need, several authors have explored the generation of random vectors with speciied marginals, together with a speciied covariance matrix, through the use of a transformation of a multivariate normal random vector. A covariance matrix is said to ...

Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR) context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory ...

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-Gaussian distribution in high dimensional setting. The proposed estimators are obtained by minimizing the quadratic loss function and joint penalty of `1 norm and variance of its eigenvalues. In contrast to some of the existing methods of covariance...

The covariance matrix of a p-dimensional random variable is a fundamental quantity in data analysis. Given n i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of O(np2) operations. When n, p are large, this computation may be prohibitively slow. Moreover, in several contemporary applications, the population matrix is approximately sparse, an...

The sandwich estimator, often known as the robust covariance matrix estimator or the empirical covariance matrix estimator, has achieved increasing use with the growing popularity of generalized estimating equations. Its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when a parametric model fails to hold, or is not even specified. Surprisin...

We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound N = O(n) for every distribution whose k-dimensional marginals have uniformly bounded 2+ε moments outside the sphere of radius O( √ k). In the specific case...

We propose an online speech source separation technique in a meeting situation. The purpose in this paper is online extraction of each speech source from multichannel microphone input signal which is contaminated by speech sources of the other persons (noise sources). The proposed method is one of adaptive beamformers. The proposed method estimates the noise covariance matrix of the multichanne...

A hierarchical Bayesian factor model for multivariate spatially correlated data is proposed. The idea behind the proposed method is to search factor scores incorporating a dependence due to a geographical structure. The great exibility of the Bayesian approach bears directly on the problem of parameter identi cation in factor analysis and furthermore on the inclusion of our prior opinion about ...