超高维异方差数据下基于边际经验似然的分位数特征筛选

Quantile screening for ultrahigh-dimensional heterogeneous data by marginal empirical likelihood

针对超高维异方差数据,基于边际经验似然提出一种分位数特征筛选方法,该方法不依赖于模型假定,且计算简单快捷,无须进行复杂的参数估计和迭代计算。同时,沿袭经验似然方法的优点,该方法对分布的假设较宽松。在一定的正则条件下,理论上证明了所提方法满足确定筛选性质。此外,为了筛选出对响应变量有影响的所有协变量,将上述方法进行推广,得到一种基于边际经验似然的分布函数特征筛选方法。最后,通过数值模拟和实例分析验证了所提出的两种方法具有良好的有限样本性质。

We propose a quantile screening method based on marginal empirical likelihood for ultrahigh-dimensional heterogeneous data.The proposed model-free method is computationally simple because it can select active predictors without parameter estimation or an iterative algorithm,and inheriting the advantages of the empirical likelihood approach results in fewer restrictive distributional assumptions.The results reveal that the proposed procedure enjoys sure screening properties under certain technical conditions.Moreover,a distribution function screening method based on marginal empirical likelihood is suggested as a way to recover the whole active predictor set.Simulation results and real data analysis confirm that the proposed screening methods perform well when used with finite samples.