Quantile feature screening for infinite dimensional data under FDR control

This study is focused on the detection of effects of features on an infinite dimensional response through the conditional spatial quantiles (CSQ) of the response given the features, and develops a novel model-free feature screening procedure for the CSQ regression function. Firstly, a new metric named kernel-based conditional quantile dependence (KCQD) is proposed to measure the dependence of the CSQ on a feature. The metric equals 0 if and only if the feature is independent of the CSQ of the response, and thus is employed to detect the contribution of a feature. Then a two-step feature screening procedure with the estimated KCQD scores is developed via a distributed strategy. Theoretical analyses reveal that the new two-step screening method not only has screening consistency and sure screening properties but also achieves control over false discovery rate (FDR). Simulation studies show its ability to control the expected FDR level while maintaining high screening power. The proposed procedure is applied to analyze a magnetoencephalography dataset, and the identified signal positions are anatomically interpretable.