Performance Bounds for Sparse Parametric Covariance Estimation in Gaussian Models

Details Performance Bounds for Sparse Parametric Covariance Estimation in Gaussian Models Performance Bounds for Sparse Parametric Covariance Estimation in Gaussian Models

2011-01-20

arxiv.org/abs/1101.3838v1

Computer Science

Information Theory

Scientific paper

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).

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