Large dimensional analysis and optimization of robust shrinkage covariance matrix estimators

JOURNAL OF MULTIVARIATE ANALYSIS

卷:131

Article

Couillet, Romain¹  McKay, Matthew² 

[1] Supelec, Dept Telecommun, Gif Sur Yvette, France

[2] Hong Kong Univ Sci & Technol, Hong Kong, Hong Kong, Peoples R China

关键词: Random matrix theory;    Robust estimation;    Linear shrinkage;   

DOI  :  10.1016/j.jmva.2014.06.018

来源: Elsevier

【 摘 要 】

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in Chen et al. (2011) and Pascal et al. (2013), based on Tyler's robust M-estimator (Tyler, 1987) and on Ledoit and Wolf's shrinkage covariance matrix estimator (Ledoit and Wolf, 2004). These hybrid estimators have the advantage of conveying (i) robustness to outliers or impulsive samples and (ii) small sample size adequacy to the classical sample covariance matrix estimator. We consider here the case of i.i.d. elliptical zero mean samples in the regime where both sample and population sizes are large. We demonstrate that, under this setting, the estimators under study asymptotically behave similar to well-understood random matrix models. This characterization allows us to derive optimal shrinkage strategies to estimate the population scatter matrix, improving significantly upon the empirical shrinkage method proposed in Chen et al. (2011). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free