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

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