Non-crossing quantile regression via monotone B-spline varying coefficients

Quantile regression can be used to obtain a nonparametric estimate of a conditional quantile function. The presence of quantile crossing, however, leads to an invalid distribution of the response and makes it dicult to use the tted model for prediction. In this work, we show that crossing can be alleviated or completely eliminated by explicit modeling of the regression coecients as a function of the percentile values in (0,1). We illustrate the approach via a wellknown dataset by emphasizing dierences with respect to the competitors.