A0429
Title: Quantile regression for functional partial linear models in high dimensions
Authors: Zhongyi Zhu - Fudan University (China) [presenting]
Abstract: A functional partial linear quantile model in high dimensional scenario is considered , where response is a scalar and predictors include multiple random processes and high-dimensional scalar covariates. A framework of regularization with two nonconvex penalty functions in the context of functional quantile regression are proposed formally, and the selection and estimation of important variables can be achieved by minimizing an double penalized functional quantile objective function. The approach proposed takes advantage of functional principal components which greatly facilitates implementation. We introduce a two-step technique for selecting tuning parameters, and establish the asymptotic oracle properties of the proposed estimators based on the difference convex analysis under some regularity conditions. The empirical performance and the usefulness of our approach are demonstrated through a large number of simulation studies and an application to air pollution data.
