Robust and efficient estimation with weighted composite quantile regression

2016 ◽  
Vol 457 ◽  
pp. 413-423 ◽  
Author(s):  
Xuejun Jiang ◽  
Jingzhi Li ◽  
Tian Xia ◽  
Wanfeng Yan
Keyword(s):  
Quantile Regression ◽  
Efficient Estimation ◽  
Composite Quantile Regression

scholarly journals Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2387
Author(s):  
Xiaoshuang Zhou ◽  
Xiulian Gao ◽  
Yukun Zhang ◽  
Xiuling Yin ◽  
Yanfeng Shen
Keyword(s):  
Quantile Regression ◽  
Asymptotic Variance ◽  
Weighted Average ◽  
Least Square ◽  
Efficient Estimation ◽  
Regression Estimator ◽  
Composite Quantile Regression ◽  
Nonparametric Function ◽  
Optimal Estimator ◽  
Better Than

In this article, we focus on the efficient estimators of the derivative of the nonparametric function in the nonparametric quantile regression model. We develop two ways of combining quantile regression information to derive the estimators. One is the weighted composite quantile regression estimator based on the quantile weighted loss function; the other is the weighted quantile average estimator based on the weighted average of quantile regression estimators at a single quantile. Furthermore, by minimizing the asymptotic variance, the optimal weight vector is computed, and consequently, the optimal estimator is obtained. Furthermore, we conduct some simulations to evaluate the performance of our proposed estimators under different symmetric error distributions. Simulation studies further illustrate that both estimators work better than the local linear least square estimator for all the symmetric errors considered except the normal error, and the weighted quantile average estimator performs better than the weighted composite quantile regression estimator in most situations.

scholarly journals Advanced algorithms for penalized quantile and composite quantile regression

2020 ◽  
Author(s):  
Matthew Pietrosanu ◽  
Jueyu Gao ◽  
Linglong Kong ◽  
Bei Jiang ◽  
Di Niu
Keyword(s):  
Quantile Regression ◽  
Composite Quantile Regression
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