Abstract #300429

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JSM 2003 Abstract #300429
Activity Number: 399
Type: Invited
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #300429
Title: Asymptotic Properties of Smoothing Parameter Selection in Spline Smoothing
Author(s): Paul L. Speckman*+ and Dongchu Sun
Companies: University of Missouri, Columbia and University of Missouri, Columbia
Address: Department of Statistics, Columbia, MO, 65211-0001,
Keywords: spline smoothing ; asymptotics ; GCV ; GML
Abstract:

Smoothing splines have achieved widespread usage as general purpose data-smoothers and are implemented in a number of statistical packages. Two methods of smoothing parameter selection are commonly used, Generalized Cross Validation (GCV) and Generalized Maximum Likelihood (GML). However, the asymptotic properties of these methods are not well understood. In this talk, we consider GCV, GML and more generally, Type II ML estimates and the marginal posterior mode. Under the usual Sobolov space frequentist assumptions on the function to be estimated, consistency and asymptotic normality of the estimated smoothing parameter are proved. The relative rates of convergence of the smoothing parameter estimates agree with those previously obtained for crossvalidated kernel density estimates. Our asymptotic results also give insight into the experimental evidence suggesting that in practice, smoothing spline estimation with GML performs better than estimation with GCV.

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