分位数回归模型中的两步变量选择

对于高维分位数回归模型提出了一种两步变量选择方法,这里协变量的维数pn远远大于样本量n.在第一步中,使用e1惩罚,并且证明第一步由LASSO惩罚所得到的惩罚估计量能够把模型从超高维降到同真实模型同阶的维数,并且所选模型能够覆盖真实模型.第二步对第一步所得模型使用自适应的LASSO惩罚来剔除冗余变量.在一些正则性条件下,证明了此方法具有变量选择的相合性.还进行了数值模拟和实际数据分析,用来表明此方法在有限样本下的表现.

Two-step variable selection in quantile regression models

We propose a two-step variable selection procedure for high dimensional quantile regressions, in which the dimension of the covariates, p_n is much larger than the sample size n. In the first step, we perform ?₁ penalty, and we demonstrate that the first step penalized estimator with the LASSO penalty can reduce the model from an ultra-high dimensional to a model whose size has the same order as that of the true model, and the selected model can cover the true model. The second step excludes the remained irrelevant covariates by applying the adaptive LASSO penalty to the reduced model obtained from the first step. Under some regularity conditions, we show that our procedure enjoys the model selection consistency. We conduct a simulation study and a real data analysis to evaluate the finite sample performance of the proposed approach.