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Simultaneous estimation of quantile regression functions using B-splines and total variation penalty

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  • Jhong, Jae-Hwan
  • Koo, Ja-Yong

Abstract

We consider the problem of simultaneously estimating a finite number of quantile functions with B-splines and the total variation penalty. For the implementation of simultaneous quantile function estimators, we develop a new coordinate descent algorithm taking into account a special structure of the total variation penalty determined by B-spline coefficients. The entire paths of solution paths for several quantile function estimators and tuning parameters can be efficiently computed using the coordinate descent algorithm. We also consider non-crossing quantile function estimators having additional constraints at the knots of spline functions. Numerical studies using both simulated and real data sets are provided to illustrate the performance of the proposed method. For a theoretical result, we prove that the proposed the quantile regression function estimators achieve the minimax rate under regularity conditions.

Suggested Citation

  • Jhong, Jae-Hwan & Koo, Ja-Yong, 2019. "Simultaneous estimation of quantile regression functions using B-splines and total variation penalty," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 228-244.
    • Handle: RePEc:eee:csdana:v:133:y:2019:i:c:p:228-244
    DOI: 10.1016/j.csda.2018.10.005
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    References listed on IDEAS

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    1. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November.
    2. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    3. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Doksum, Kjell & Koo, Ja-Yong, 2000. "On spline estimators and prediction intervals in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 35(1), pages 67-82, November.
    6. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    7. Jean–Michel Loubes & Sara Van De Geer, 2002. "Adaptive estimation with soft thresholding penalties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(4), pages 453-478, November.
    8. Roger Koenker & Ivan Mizera, 2004. "Penalized triograms: total variation regularization for bivariate smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 145-163, February.
    9. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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