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Activity Number: 543
Type: Contributed
Date/Time: Thursday, August 2, 2007 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #309537
Title: Asymptotic Theory of Bivariate Penalized Splines
Author(s): Yingxing Li*+ and David Ruppert
Companies: Cornell University and Cornell University
Address: 301 Malott Hall, Ithaca, NY, 14850,
Keywords: Asymptotic bias ; B-splines ; Difference penalty ; Number of knots ; backfitting
Abstract:

We study the asymptotic behavior of penalized spline estimators in the bivariate case. Tensor-product B-splines are used and a penalty is placed on the differences of the coefficients. By choosing an appropriate penalty, the estimator has the same convergent rate as in the univariate nonparametric regression. Providing that the number of knots converges to infinity fast enough, the number of knots does not affect the asymptotic distribution. Expressions for the bias and variance are given. The results are compared to backfitting.

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Revised September, 2007