Estimation of a sparse and spiked covariance matrix
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Detail(s)
Original language | English |
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Pages (from-to) | 241-252 |
Journal / Publication | Journal of Nonparametric Statistics |
Volume | 27 |
Issue number | 2 |
Publication status | Published - 3 Apr 2015 |
Externally published | Yes |
Link(s)
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.
In: Journal of Nonparametric Statistics, Vol. 27, No. 2, 03.04.2015, p. 241-252.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review