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We introduce a quantile-adaptive framework for nonlinear variable screeningwith high-dimensional heterogeneous data. This framework has two distinctivefeatures: (1) it allows the set of active variables to vary across quantiles,thus making it more flexible to accommodate heterogeneity; (2) it is model-freeand avoids the difficult task of specifying the form of a statistical model ina high dimensional space. Our nonlinear independence screening procedureemploys spline approximations to model the marginal effects at a quantile levelof interest. Under appropriate conditions on the quantile functions withoutrequiring the existence of any moments, the new procedure is shown to enjoy thesure screening property in ultra-high dimensions. Furthermore, thequantile-adaptive framework can naturally handle censored data arising insurvival analysis. We prove that the sure screening property remains valid whenthe response variable is subject to random right censoring. Numerical studiesconfirm the fine performance of the proposed method for various semiparametricmodels and its effectiveness to extract quantile-specific information fromheteroscedastic data.

Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data