Joint modelling of non-crossing additive quantile regression via constrained B-spline varying coefficients

We present a unified framework able to fit the entire quantile process, namely to estimate simultaneously multiple non-crossing quantile curves. The framework relies on assuming each regression parameter varies smoothly across the percentile direction according to B-splines whose coefficients obey proper restrictions. Multiple linear and penalized smooth terms are allowed and the corresponding tuning parameters are estimated efficiently as part of the model fitting. Monotonicity and concavity constraints on the smoothed relationships are also easily accounted for in the framework. Simulation results provide evidence our proposal exhibits good statistical performance with respect to competitors while guaranteeing the non-crossing property and modest computational load. Analyses on a real dataset related to vocabulary size growth are presented to illustrate the model capability in practice.