Robust Estimation of Generalized Additive Models

• Activity Number: 333
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Raymond Ka Wai Wong*+ and Fang Yao and Thomas C. M. Lee
• Companies: University of California at Davis and University of Toronto and University of California at Davis
• Keywords: Bounded score function ; Generalized information criterion ; Generalized linear model ; Robust estimating equation ; Robust quasi-likelihood ; Smoothing parameter selection

Abstract

This article studies M-type estimators for fitting generalized additive models in the presence of anomalous data. A new theoretical construct is developed to link the costly M-type calculations with least-squares type computations. Its asymptotic properties are studied and used to motivate a computational algorithm. The main idea is to decompose the overall M-type estimation problem into a sequence of well-studied conventional additive model fittings. The resulting algorithm is fast and stable, can be paired with different nonparametric smoothers, and can also be applied to cases with multiple covariates. As another contribution of this article, automatic methods for smoothing parameter selection are proposed. These methods are designed to be resistant to outliers. The empirical performance of the proposed methodology is illustrated via both simulation experiments and real data analysis.