Simultaneous estimation of linear conditional quantiles with penalized splines

Heng Lian, Jie Meng and Zengyan Fan

Journal of Multivariate Analysis, 2015, vol. 141, issue C, 1-21

Abstract: 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.

Keywords: Gaussian process; Quantile process; Spline approximation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.jmva.2015.06.010

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