Estimation of a sparse and spiked covariance matrix

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)241-252
Journal / PublicationJournal of Nonparametric Statistics
Volume27
Issue number2
Publication statusPublished - 3 Apr 2015
Externally publishedYes

Abstract

We suggest a method for estimating a covariance matrix that can be represented as a sum of a sparse low-rank matrix and a diagonal matrix. Our formulation is based on penalized quadratic loss, which is a convex problem that can be solved via incremental gradient and proximal method. In contrast to other spiked covariance matrix estimation approaches that are related to principal component analysis and factor analysis, our method has a simple formulation and does not constrain entire rows and columns of the matrix to be zero. We further discuss a penalized entropy loss method that is nevertheless nonconvex and necessitates a majorization-minimization algorithm in combination with the incremental gradient and proximal method. We carry out simulations to demonstrate the finite-sample properties focusing on high-dimensional covariance matrices. Finally, the proposed method is illustrated using a gene expression data set.

Research Area(s)

  • cross-validation, factor analysis, nuclear norm, principal component analysis, sparsity norm

Citation Format(s)

Estimation of a sparse and spiked covariance matrix. / Lian, Heng; Fan, Zengyan.
In: Journal of Nonparametric Statistics, Vol. 27, No. 2, 03.04.2015, p. 241-252.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review