Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
Abstract
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a data-driven weighted linear combination of convex loss functions, together with weighted -penalty. It is completely data-adaptive and does not require prior knowledge of the error distribution. The weighted -penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias caused by the -penalty. In the setting with dimensionality much larger than the sample size, we establish a strong oracle property of the proposed method that possesses both the model selection consistency and estimation efficiency for the true non-zero coefficients. As specific examples, we introduce a robust method of composite L1-L2, and optimal composite quantile method and evaluate their performance in both simulated and real data examples.
Cite
@article{arxiv.0912.5200,
title = {Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection},
author = {Jelena Bradic and Jianqing Fan and Weiwei Wang},
journal= {arXiv preprint arXiv:0912.5200},
year = {2011}
}