Robust estimation of high-dimensional covariance and precision matrices
File(s)
Accepted version
Author(s)
Avella, Marco
Battey, HS
Fan, Jianqing
Li, Quefeng
Type
Journal Article
Abstract
High-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+ϵ
moments for
ϵ∈(0,2)
. The associated convergence rates depend on
ϵ
.
2+ϵ
moments for
ϵ∈(0,2)
. The associated convergence rates depend on
ϵ
.
Date Issued
2018-06-01
Date Acceptance
2018-01-15
Citation
Biometrika, 2018, 105 (2), pp.271-284
ISSN
0006-3444
Publisher
Oxford University Press (OUP)
Start Page
271
End Page
284
Journal / Book Title
Biometrika
Volume
105
Issue
2
Copyright Statement
© 2018 Biometrika Trust. This is a pre-copy-editing, author-produced version of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version is available online at: https://academic.oup.com/biomet/article/105/2/271/4955410
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/P002757/1
EP/P002757/1
Subjects
Statistics & Probability
0103 Numerical and Computational Mathematics
0104 Statistics
1403 Econometrics
Publication Status
Published
Date Publish Online
2018-03-27