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

Jae-Hwan Jhong and Ja-Yong Koo

Computational Statistics & Data Analysis, 2019, vol. 133, issue C, 228-244

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.

Keywords: Binary method; Coordinate descent algorithm; Minimax rate; Non-crossing; Total variation; Weighted quantile (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:133:y:2019:i:c:p:228-244

DOI: 10.1016/j.csda.2018.10.005

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