Simultaneous estimation of linear conditional quantiles with penalized splines
journal contribution
posted on 2021-11-05, 12:26authored byHeng Lian, Jie MengJie Meng, Zengyan Fan
We consider smooth estimation of the conditional quantile process in linear models using penalized splines. For linear quantile regression problems, usually separate models are fitted at a finite number of quantile levels and then information from different quantiles is combined in interpreting the results. We propose a smoothing method based on penalized splines that computes the conditional quantiles all at the same time. We consider both fixed-knots and increasing-knots asymptotics of the estimator and show that it converges to a multivariate Gaussian process. Simulations show that smoothing can result in more accurate estimation of the conditional quantiles. The method is further illustrated on a real data set. Empirically (although not theoretically) we observe that the crossing quantile curves problem can often disappear using the smoothed estimator.
This paper was accepted for publication in the journal Journal of Multivariate Analysis and the definitive published version is available at https://doi.org/10.1016/j.jmva.2015.06.010.