Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 122, Issue -, Pages 115-132Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2013.07.015
Keywords
B-spline; High dimensional; LASSO; Linear programming; Nonparametric
Categories
Funding
- Natural Science Foundation of China [11271080]
- Hong Kong Special Administration Region [GRF 403109]
- National Science Foundation (NSF) [DMS-10-07420]
- NSF CAREER Award [DMS-114935]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1149355] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1007420] Funding Source: National Science Foundation
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In this paper, we propose a two-stage variable selection procedure for high dimensional quantile varying coefficient models. The proposed method is based on basis function approximation and LASSO-type penalties. We show that the first stage penalized estimator with LASSO penalty reduces the model from ultra-high dimensional to a model that has size close to the true model, but contains the true model as a valid sub model. By applying adaptive LASSO penalty to the reduced model, the second stage excludes the remained irrelevant covariates, leading to an estimator consistent in variable selection. A simulation study and the analysis of a real data demonstrate that the proposed method performs quite well in finite samples, with regard to dimension reduction and variable selection. (C) 2013 Elsevier Inc. All rights reserved.
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