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- Title
Partial estimation of covariance matrices.
- Authors
Levina, Elizaveta; Vershynin, Roman
- Abstract
A classical approach to accurately estimating the covariance matrix Σ of 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 $${n \ll p}$$. We show that a sample of size n = O( m log p) is sufficient to accurately estimate in operator norm an arbitrary symmetric part of Σ consisting of m ≤ n nonzero entries per row. This follows from a general result on estimating Hadamard products M · Σ, where M is an arbitrary symmetric matrix.
- Subjects
ESTIMATION theory; COVARIANCE matrices; DISTRIBUTION (Probability theory); MATHEMATICAL symmetry; OPERATOR theory; APPLIED mathematics; MATHEMATICAL analysis
- Publication
Probability Theory & Related Fields, 2012, Vol 153, Issue 3/4, p405
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-011-0349-4