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Title: Asymptotic properties of penalized spline estimators
Authors: Claeskens, Gerda ×
Krivobokova, Tatyana
Opsomer, Jean #
Issue Date: 2009
Publisher: University Press
Series Title: Biometrika vol:96 issue:3 pages:529-544
Abstract: We study the class of penalized spline estimators, which enjoy similarities to both regression splines, without penalty and with fewer knots than data points, and smoothing splines, with knots equal to the data points and a penalty controlling the roughness of the fit. Depending on the number of knots, sample size and penalty, we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of smoothing splines, with a clear breakpoint distinguishing the cases. We prove that using fewer knots results in better asymptotic rates than when using a large number of knots. We obtain expressions for bias and variance and asymptotic rates for the number of knots and penalty parameter.
ISSN: 0006-3444
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Research Center for Operations Research and Business Statistics (ORSTAT), Leuven
× corresponding author
# (joint) last author

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