CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2014, 30(5) 537-560 DOI:      ISSN: 1001-4268 CN: 31-1256

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Variable Selection of Quantile Varying Coefficient Models Based on Kernel Smoothing

Zhao Weihua, Zhang Riquan, Liu Jicai

School of Science, Nantong University; School of Finance and Statistics, East China Normal University; Department of Mathematics, Shanxi Datong University

Abstract��

Quantile varying coefficient model is one of the robust
nonparametric modeling method. When one uses varying coefficient model to analyze data,
a natural question is how to simultaneously select the relevant variables and separate
the nonzero constant effect variables from nonzero varying effect variables. In this
paper, we address the problem of both robustness and efficiency of estimation and variable
selection procedure based on quantile regression. By combining the idea of the local
kernel modeling and adaptive group Lasso method, we obtain penalized estimation through
imposing double penalties on the quantile check function. With appropriate selection of
tuning parameters by BIC criterion, the theoretical properties of the new variable
selection procedure can be established. The finite sample performance of the new method
is investigated through simulation studies and the analysis of body fat data. Numerical
studies show that the new method can simultaneously identify unimportant variables and
separate non-varying coefficient variables among important variables without any prior
information about variables and irrespective of model error distribution.

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