Abstract #300882

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JSM 2003 Abstract #300882
Activity Number: 210
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #300882
Title: P Spline Smoothing and Mixed Models
Author(s): Goeran Kauermann*+
Companies: University Bielfeld
Address: Department of Economics, 33501 Bielefeld, , , Germany
Keywords: bandwidth selection ; linear mixed models ; P spline smoothing
Abstract:

For spline-based smoothing, one can rewrite the smooth estimation as a linear mixed model, where the smoothing parameter appears as "a priori" variance of the spline basis coefficients.This allows one to employ maximum likelihood (ML) theory to estimate the smoothing parameter as variance component. We illuminate this relation in more depth for penalized spline smoothing (P spline), as suggested in Eilers and Marx (Stat. Science, 1996). Theoretical and empirical arguments are given, showing that the ML approach for choosing the bandwidth is biased toward overfitting. This result is in contrast to findings for classical spline smoothing, where ML selected bandwidths tend to oversmooth. The reason for this disagreement is that in P spline smoothing a finite dimensional basis is employed, while in classical spline smoothing the basis grows with the sample size. As a consequence, the approaches show different asymptotic as well as small sample behavior. Simulations and some data examples are given to support the theoretical findings

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