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Title: Bootstrapping for penalized spline regression
Authors: Claeskens, Gerda
Kauermann, G
Opsomer, JD
Issue Date: 2006
Publisher: K.U.Leuven - Faculty of Economics and Applied Economics
Series Title: DTEW - KBI_0609 pages:1-30
Abstract: We describe and contrast several different bootstrapping procedures for penalized spline smoothers. The bootstrapping procedures considered are variations on existing methods, developed under two different probabilistic frameworks. Under the first framework, penalized spline regression is considered an estimation technique to find an unknown smooth function. The smooth function is represented in a high dimensional spline basis, with spline coefficients estimated in a penalized form. Under the second framework, the unknown function is treated as a realization of a set of random spline coefficients, which are then predicted in a linear mixed model. We describe how bootstrapping methods can be implemented under both frameworks, and we show in theory and through simulations and examples that bootstrapping provides valid inference in both cases. We compare the inference obtained under both frameworks, and conclude that the latter generally produces better results than the former. The bootstrapping ideas are extended to hypothesis testing, where parametric components in a model are tested against nonparametric alternatives.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Research Center for Operations Research and Business Statistics (ORSTAT), Leuven

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