A Note on Choosing the Threshold for Large Covariance Estimations in Factor Models

Yuan Liao

doi:10.48550/arxiv.1608.08318

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A Note on Choosing the Threshold for Large Covariance Estimations in Factor Models

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A Note on Choosing the Threshold for Large Covariance Estimations in Factor Models

Yuan Liao

ArXiv.org

Cornell University

08/30/2016

DOI: 10.48550/arxiv.1608.08318

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

This note shows that for i.i.d. data, estimating large covariance matrices in factor models can be casted using a simple plug-in method to choose the threshold: μjl = c0 √n Φ−1(1 – α 2p2 ) √ √ √ √ 1 n n∑ i=1̂ u2 jî u2 li. This is motivated by the tuning parameter suggested by Belloni et al. (2012) in the lasso literature. It also leads to the minimax rate of convergence of the large covariance matrix estimator. Previously, the minimaxity is achievable only when n = o(p log p) by Fan et al. (2013), and now this condition is weakened to n = o(p2 log p). Here n denotes the sample size and p denotes the dimension.

Statistics - Methodology

Details

Title: Subtitle: A Note on Choosing the Threshold for Large Covariance Estimations in Factor Models
Creators: Yuan Liao
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.1608.08318
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 08/30/2016
Academic Unit: Economics
Record Identifier: 9984937927202771

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