Partial estimation of covariance matrices

• 成果类型: Article
• 署名作者: Levina, Elizaveta; Vershynin, Roman
• 署名单位: University of Michigan System; University of Michigan; University of Michigan System; University of Michigan
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0349-4
• 发表日期: 2012
• 页码: 405-419
• 关键词: smallest eigenvalue; regularization; limit; NORM

摘要

A classical approach to accurately estimating the covariance matrix I pound 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 . 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 I pound consisting of m a parts per thousand currency sign n nonzero entries per row. This follows from a general result on estimating Hadamard products M center dot I pound, where M is an arbitrary symmetric matrix.