A note on quantile feature screening via distance correlation

In this paper, we propose a new feature screening procedure based on a robust quantile version of distance correlation with some desirable characters. First, it is particularly useful for data exhibiting heterogeneity, which is very common for high dimensional data. Second, it is robust to model misspecification and behaves reliably when some of features contain outliers or follow heavy-tailed distributions. Under very mild conditions, we have established its sure screening property. In practice, a same index set is often found to be adequate by the quantile analysis. So we furthermore present a composite robust quantile version of distance correlation to perform feature screening. Simulation studies are carried out to examine the performance of advised procedures. We also illustrate them by a real data example.

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