Open Access
September 2013 Robust regularized singular value decomposition with application to mortality data
Lingsong Zhang, Haipeng Shen, Jianhua Z. Huang
Ann. Appl. Stat. 7(3): 1540-1561 (September 2013). DOI: 10.1214/13-AOAS649


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 leave-one-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.


Download Citation

Lingsong Zhang. Haipeng Shen. Jianhua Z. Huang. "Robust regularized singular value decomposition with application to mortality data." Ann. Appl. Stat. 7 (3) 1540 - 1561, September 2013.


Published: September 2013
First available in Project Euclid: 3 October 2013

zbMATH: 06237187
MathSciNet: MR3127958
Digital Object Identifier: 10.1214/13-AOAS649

Keywords: cross-validation , Functional data analysis , GCV , Principal Component Analysis , robustness , smoothing spline

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 3 • September 2013
Back to Top