The Annals of Applied Statistics

Robust regularized singular value decomposition with application to mortality data

Lingsong Zhang, Haipeng Shen, and Jianhua Z. Huang

Full-text: Open access

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 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.

Article information

Source
Ann. Appl. Stat., Volume 7, Number 3 (2013), 1540-1561.

Dates
First available in Project Euclid: 3 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1380804806

Digital Object Identifier
doi:10.1214/13-AOAS649

Mathematical Reviews number (MathSciNet)
MR3127958

Zentralblatt MATH identifier
06237187

Keywords
Cross-validation functional data analysis GCV principal component analysis robustness smoothing spline

Citation

Zhang, Lingsong; Shen, Haipeng; Huang, Jianhua Z. Robust regularized singular value decomposition with application to mortality data. Ann. Appl. Stat. 7 (2013), no. 3, 1540--1561. doi:10.1214/13-AOAS649. https://projecteuclid.org/euclid.aoas/1380804806


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Supplemental materials

  • Supplementary material: Supplemental notes for “Robust regularized singular value decomposition with application to mortality data”. The supplemental notes include deviation of the GCV formula in this paper, an MM algorithm to handle missing value, two additional simulation examples in details, and one additional plot for the analysis of the mortality data.