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Simultaneous estimation of linear conditional quantiles with penalized splines

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  • Lian, Heng
  • Meng, Jie
  • Fan, Zengyan

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.

Suggested Citation

  • Lian, Heng & Meng, Jie & Fan, Zengyan, 2015. "Simultaneous estimation of linear conditional quantiles with penalized splines," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 1-21.
    • Handle: RePEc:eee:jmvana:v:141:y:2015:i:c:p:1-21
    DOI: 10.1016/j.jmva.2015.06.010
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    5. Feng, Xingdong & Liu, Qiaochu & Wang, Caixing, 2023. "A lack-of-fit test for quantile regression process models," Statistics & Probability Letters, Elsevier, vol. 192(C).

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