B1233
Title: Partially linear additive quantile regression in ultra-high dimension
Authors: Lan Wang - University of Minnesota (United States) [presenting]
Abstract: We consider flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. The sparsity level is allowed to be different at different quantile levels. We approximate the nonlinear components using B-spline basis functions. We first study estimation under this model when the nonzero components are known in advance and the number of covariates in the linear part diverges. We then investigate a non-convex penalized estimator for simultaneous variable selection and estimation. We derive its oracle property for a general class of non-convex penalty functions in the presence of ultra-high dimensional covariates under relaxed conditions. To tackle the challenges of nonsmooth loss function, non-convex penalty function and the presence of nonlinear components, we combine a recently developed convex-differencing method with modern empirical process techniques. We also discuss how the method for a single quantile of interest can be extended to simultaneous variable selection and estimation at multiple quantiles.
