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Activity Number: 42
Type: Invited
Date/Time: Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #302945
Title: Simultaneous Confidence Bands for Penalized Spline Estimators
Author(s): Tatyana Krivobokova*+ and Thomas Kneib and Gerda Claeskens
Companies: Georg-August-Universitaet Goettingen and Ludwig-Maximilains-Universitaet Muenchen and Katholieke Universiteit Leuven
Address: , , ,
Keywords: confidence band ; penalized splines ; volume-of-tube formula
Abstract:

In this paper we construct simultaneous confidence bands for a smooth curve using penalized splines. For the curve estimation a standard nonparametric regression model is used, as well as the mixed model formulation of penalized splines. The Hotelling's (1939) volume-of-tube formula is applied for the construction of approximate simultaneous confidence bands in both models, showing the advantages of the mixed model representation of penalized splines. The choice of the smoothing parameter is discussed. Finally, a Bayesian formulation of penalized splines is considered and a new approach for the construction of simultaneous credible bands is proposed. Simulations and data analysis illustrate and compare all methods considered. The R package ConfBands accompanies the paper.

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