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February 2020 Robust sparse covariance estimation by thresholding Tyler’s M-estimator
John Goes, Gilad Lerman, Boaz Nadler
Ann. Statist. 48(1): 86-110 (February 2020). DOI: 10.1214/18-AOS1793

Abstract

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental task in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Toward bridging this gap, in this work we consider estimating a sparse shape matrix from $n$ samples following a possibly heavy-tailed elliptical distribution. We propose estimators based on thresholding either Tyler’s M-estimator or its regularized variant. We prove that in the joint limit as the dimension $p$ and the sample size $n$ tend to infinity with $p/n\to\gamma>0$, our estimators are minimax rate optimal. Results on simulated data support our theoretical analysis.

Citation

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John Goes. Gilad Lerman. Boaz Nadler. "Robust sparse covariance estimation by thresholding Tyler’s M-estimator." Ann. Statist. 48 (1) 86 - 110, February 2020. https://doi.org/10.1214/18-AOS1793

Information

Received: 1 June 2017; Revised: 1 November 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196531
MathSciNet: MR4065154
Digital Object Identifier: 10.1214/18-AOS1793

Subjects:
Primary: 62H12
Secondary: 62G20, 62G35

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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