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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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    Cited by:

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    4. Ta‐Hsin Li, 2021. "Quantile‐frequency analysis and spectral measures for diagnostic checks of time series with nonlinear dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 270-290, March.
    5. Cheng Peng & Stanislav Uryasev, 2023. "Factor Model of Mixtures," Papers 2301.13843, arXiv.org, revised Mar 2023.

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