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Estimation of a sparse and spiked covariance matrix

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  • Heng Lian
  • Zengyan Fan

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.

Suggested Citation

  • Heng Lian & Zengyan Fan, 2015. "Estimation of a sparse and spiked covariance matrix," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 241-252, June.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:241-252
    DOI: 10.1080/10485252.2015.1022545
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    Cited by:

    1. Avagyan, Vahe, 2016. "D-Trace precision matrix estimator with eigenvalue control," DES - Working Papers. Statistics and Econometrics. WS 23410, Universidad Carlos III de Madrid. Departamento de Estadística.

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