An Effective Nonparametric Quantile Regression Method for Solving the Crossing Problem in Data Fitting Process

Abstract

Nonparametric quantile regression method can be used as the first choice for some biostatistical data. Since the nonparametric quantile regression curves are estimated individually, the quantile curves can cross, leading to an invalid distribution estimation for the response. A simple nonparametric quantile regression method is proposed to avoid the crossing problem. The method uses nonparametric conditional density function estimate instead of the conditional distribution estimate to assure quantile regression function monotonous. Both a simulation study and an analysis of real salmon lustrousness data show the significant improvement of the method in solving the quantile crossing problem for some kind of biological data.