LOCAL COMPOSITE QUANTILE REGRESSION SMOOTHING: A FLEXIBLE DATA STRUCTURE AND CROSS-VALIDATION

2020 ◽  
pp. 1-19
Author(s):  
Xiao Huang ◽  
Zhongjian Lin
Keyword(s):  
Data Structure ◽  
Quantile Regression ◽  
Empirical Studies ◽  
Linear Estimator ◽  
Polynomial Method ◽  
Regression Estimator ◽  
Composite Quantile Regression ◽  
Safe Alternative ◽  
Continuous Covariates ◽  
The Cross

In this paper, we study the local composite quantile regression estimator for mixed categorical and continuous data. The local composite quantile estimator is an efficient and safe alternative to the local polynomial method and has been well-studied for continuous covariates. Generalization of the local composite quantile regression estimator to a flexible data structure is appealing to practitioners as empirical studies often encounter categorical data. Furthermore, we study the theoretical properties of the cross-validated bandwidth selection for the local composite quantile estimator. Under mild conditions, we derive the rates of convergence of the cross-validated smoothing parameters to their optimal benchmark values for both categorical and continuous covariates. Monte Carlo experiments show that the proposed estimator may have large efficiency gains compared with the local linear estimator. Furthermore, we illustrate the robustness of the local composite quantile estimator using the Boston housing dataset.

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.

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