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arXiv · 1008.1716

Partial estimation of covariance matrices

Elizaveta Levina·Roman Vershynin
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Abstract

A classical approach to accurately estimating the covariance matrix Σof a p-variate normal distribution is to draw a sample of size n > p and form a sample covariance matrix. However, many modern applications operate with much smaller sample sizes, thus calling for estimation guarantees in the regime n << p. We show that a sample of size n = O(m log^6 p) is sufficient to accurately estimate in operator norm an arbitrary symmetric part of Σconsisting of m < n entries per row. This follows from a general result on estimating Hadamard products M.Σ, where M is an arbitrary symmetric matrix.

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Elizaveta Levina, Roman Vershynin. 2011-02-11. Partial estimation of covariance matrices. https://arxiv.org/abs/1008.1716

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