Quantile Screening For Ultrahigh-dimensional Heterogeneous Data By Marginal Empirical Likelihood

With the development of modern science and technology and the improvement of storage technology,ultra-high dimensional data has been widely used in fields such as gene expression,signal processing,financial analysis and so on.The ultra-high dimension brings severe challenges in computing performance and methodology.At present,there are some problems in ultra-high dimensional data,such as high collinearity,pseudo correlation and noise accumulation.Therefore,feature selection and variable selection have become one of the most basic problems in ultra-high dimensional data analysis.In this paper,we propose a quantile screening method based on marginal empirical likelihood for ultrahigh-dimensional heterogeneous data.We combine quantile regression with empirical likelihood without relying on the model assumption.The proposed model-free method is computationally simple because it can select active predictors without parameter estimation and iterative algorithm,and it is very convenient in theoretical analysis and practical application.In the meanwhile,there are less restrictive distributional assumptions by inheriting the advantage of empirical likelihood approach.The theoretical result reveal that the proposed procedure enjoys the sure screening property under certain technical conditions.Moreover,a distribution function screening method based on marginal empirical likelihood is suggested to recover the whole active predictor set.Simulation results and real data analysis confirm that the proposed screening methods have good performance in finite samples.The proposed method can better solve the problem of data heterogeneity and can recover active variables in ultra-high-dimensional data.