A1309
Title: Nonparametric estimation of non-crossing quantile regression process with deep ReQU neural networks
Authors: Guohao Shen - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Yuling Jiao - Wuhan University (China)
Yuanyuan Lin - The Chinese University of Hong Kong (Hong Kong)
Joel Horowitz - Northwestern University (United States)
Jian Huang - The Hong Kong Polytechnic University (China)
Abstract: A penalized nonparametric approach is proposed to estimate the quantile regression process (QRP) in a nonseparable model using rectified quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce the non-crossing of quantile regression curves. The non-asymptotic excess risk bounds for the estimated QRP are established, and the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions are derived. A new error bound for approximating $C^s$ smooth functions with $s > 0$ and their derivatives using ReQU-activated neural networks is also developed to establish these non-asymptotic risk and estimation error bounds. This is a new approximation result for ReQU networks and is of independent interest, and may be useful in other problems. The numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests for nonparametric quantile regression.
