Fast and Stable Multiple Smoothing Parameter Selection in Smoothing Spline Analysis of Variance Models with Large Samples

• Activity Number: 292
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Nathaniel Helwig*+ and Ping Ma
• Companies: University of Illinois and University of Illinois at Urbana-Champaign
• Keywords: Smoothing splines ; SSANOVA ; Multivariate smoothing ; Semiparametric regression ; Large sample methods

Abstract

The current parameterization and algorithm used to fit a smoothing spline analysis of variance (SSANOVA) model are computationally expensive, making a generalized additive model (GAM) the preferred method for multivariate smoothing. In this paper, we propose an efficient parameterization of the smoothing parameters in SSANOVA models, which can greatly stabilize and speed-up the fitting of the model. We also propose a faster algorithm for estimating multiple smoothing parameters in SSANOVAs. To validate our approach, we present a simulation study comparing our reparameterization and algorithm to implementations of SSANOVAs and GAMs that are currently available in R. Our simulation results reveal that SSANOVAs can outperform GAMs when smoothing multivariate data, and, using our efficient parameterization and algorithm, an SSANOVA model can be fit in a similar amount of time as the corresponding GAM. Thus, SSANOVAs should be preferred for multivariate smoothing.