Robust regularized singular value decomposition with application to mortality data

Lingsong Zhang, Haipeng Shen, Jianhua Z. Huang

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13 Scopus citations

Abstract

We develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The RobRSVD is formulated as a penalized loss minimization problem where a robust loss function is used to measure the reconstruction error of a low-rank matrix approximation of the data, and an appropriately defined two-way roughness penalty function is used to ensure smoothness along each of the two functional domains. By viewing the minimization problem as two conditional regularized robust regressions, we develop a fast iterative reweighted least squares algorithm to implement the method. Our implementation naturally incorporates missing values. Furthermore, our formulation allows rigorous derivation of leaveone- row/column-out cross-validation and generalized cross-validation criteria, which enable computationally efficient data-driven penalty parameter selection. The advantages of the new robust method over nonrobust ones are shown via extensive simulation studies and the mortality rate application. © Institute of Mathematical Statistics, 2013.
Original languageEnglish (US)
Pages (from-to)1540-1561
Number of pages22
JournalThe Annals of Applied Statistics
Volume7
Issue number3
DOIs
StatePublished - Sep 2013
Externally publishedYes

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