Robust estimation of high-dimensional covariance and precision matrices

Marco Avella-Medina, Heather S Battey, Jianqing Fan and Quefeng Li

Biometrika, 2018, vol. 105, issue 2, 271-284

Abstract: SUMMARYHigh-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a bounded fourth moment assumption, achieve the same minimax convergence rates as do existing methods under a sub-Gaussianity assumption. Consistency of the proposed estimators is also established under the weak assumption of bounded $2+\epsilon$ moments for $\epsilon\in (0,2)$. The associated convergence rates depend on $\epsilon$.

Keywords: Constrained ℓ1-minimization; Leptokurtosis; Minimax rate; Robustness; Thresholding (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (13)

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