Performance Bounds for Sparse Parametric Covariance Estimation in Gaussian Models
Information Theory
2011-01-21 v1 math.IT
Statistics Theory
Statistics Theory
Abstract
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower bounds on the variance of estimators with a given mean function. This includes unbiased estimation as a special case. We also present a numerical comparison of our lower bounds with the variance of two standard estimators (hard-thresholding estimator and maximum likelihood estimator).
Cite
@article{arxiv.1101.3838,
title = {Performance Bounds for Sparse Parametric Covariance Estimation in Gaussian Models},
author = {Alexander Jung and Sebastian Schmutzhard and Franz Hlawatsch and Alfred O. Hero},
journal= {arXiv preprint arXiv:1101.3838},
year = {2011}
}