Title: Quantile regression for functional partially linear models in ultra-high dimensions
Authors: Haiqiang Ma - Jiangxi University of Finance and Economics (China) [presenting]
Abstract: A functional partially linear quantile model in ultra-high dimensional scenarios is considered, where the response is scalar and the predictors include both multiple random processes and high-dimensional scalar covariates. A framework of regularization with two nonconvex penalty functions in the context of functional partially linear quantile regression is proposed formally, and the selection and estimation of important variables can be then achieved by minimizing a double penalized functional quantile objective function. In a theoretical investigation, we establish the asymptotic properties of the resulting estimators based on the difference convex analysis (DCA) under some regularity conditions, and also consider the convergence rate of the prediction of the conditional quantile function. The empirical performance and the usefulness of our proposed approach are demonstrated through a large number of simulation studies and a real application.