Reduced rank stochastic regression with a sparse singular value decomposition

Kun Chen, Kung-Sik Chan, Nils Chr. Stenseth

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2012 · Volume 74 · Issue 2

DOI: 10.1111/j.1467-9868.2011.01002.x

Abstract

Summary.For a reduced rank multivariate stochastic regression model of rankr*, the regression coefficient matrix can be expressed as a sum ofr*unit rank matrices each of which is proportional to the outer product of the left and right singular vectors. For improving predictive accuracy and facilitating interpretation, it is often desirable that these left and right singular vectors be sparse or enjoy some smoothness property. We propose a regularized reduced rank regression approach for solving this problem. Computation algorithms and regularization parameter selection methods are developed, and the properties of the new method are explored both theoretically and by simulation. In particular, the regularization method proposed is shown to be selection consistent and asymptotically normal and to enjoy the oracle property. We apply the proposed model to perform biclustering analysis with microarray gene expression data.

Keywords

Biclustering, Microarrary gene expression data, Multivariate regression, Oracle property, Regularization

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