Adaptive penalized quantile regression for high dimensional data

作者：Zheng Qi^*; Gallagher Colin; Kulasekera K B

来源：Journal of Statistical Planning and Inference, 2013, 143(6): 1029-1038.

DOI：10.1016/j.jspi.2012.12.009

• Adaptive
• Quantile regression
• Oracle rate
• Asymptotic normality
• Variable selection

We propose a new adaptive L-1 penalized quantile regression estimator for high-dimensional sparse regression models with heterogeneous error sequences. We show that under weaker conditions compared with alternative procedures, the adaptive L-1 quantile regression selects the true underlying model with probability converging to one, and the unique estimates of nonzero coefficients it provides have the same asymptotic normal distribution as the quantile estimator which uses only the covariates with nonzero impact on the response. Thus, the adaptive L-1 quantile regression enjoys oracle properties. We propose a completely data driven choice of the penalty level lambda(n), which ensures good performance of the adaptive L-1 quantile regression. Extensive Monte Carlo simulation studies have been conducted to demonstrate the finite sample performance of the proposed method.

• 出版日期2013-6