Conditional quantile correlation screening procedure for ultrahigh-dimensional varying coefficient models

Abstract

Ultrahigh-dimensional variable screening plays an increasingly important part in diverse scientific areas and statistical researches. This paper mainly proposes two new feature screening approaches for varying coefficient models in ultrahigh-dimensional data analysis. One of them use the conditional quantile correlation corresponding to CQSISτ as an utility measure of importance between the τth quantile of response and predictor conditioning on the index variable, and the other utilizes the conditional distribution correlation, which corresponds to CQSIS, as an utility measure of significance between the response and predictor conditioning on the index variable. Under some regularization conditions, we establish the theoretical properties, including ranking consistency property and sure screening property. Simulation studies are conducted to evaluate the performance of the proposed methodologies. The simulations results show that our proposed approaches CQSISτ and CQSIS significantly outperforms the existing methods in terms of varying coefficient models. We also illustrate the performance of CQSISτ and CQSIS through two real-data examples. Both theoretical and numerical studies demonstrate the effectiveness of the proposed methods.