Statistical Modelling 11 (2011), 409427
Variable selection in partially linear wavelet models
Huijuan Ding
ORSTAT and Leuven Statistics Research Center
K.U.Leuven
Belgium
Gerda Claeskens
ORSTAT and Leuven Statistics Research Center
K.U.Leuven
Naamsestraat 69
B3000 Leuven
Belgium
eMail: gerda.claeskens@econ.kuleuven.be
Maarten Jansen
Departments of Mathematics and Computer Science
Università Libre de Bruxelles
Belgium
Abstract:
Variable selection is fundamental in high-dimensional statistical modelling,
including non-and semiparametric regression. However, little work has been
done for variable selection in a partially linear model (PLM). We propose and
study a unified approach via double penalized least squares, retaining good
features of both variable selection and model estimation in the framework of
PLM. The proposed method is distinguished from others in that the penalty
functions combine the l 1 penalty coming from wavelet thresholding in the
non-parametric component with the l 1 penalty from the lasso in the parametric
component. Simulations are used to investigate the performances of the
proposed estimator in various settings, illustrating its effectiveness for
simultaneous variable selection as well as estimation.
Keywords:
lasso; l1 penalty; partially linear model; variable selection; wavelet
estimation
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