New estimation method to reduce the high leverage points effect in quantile regression

Document Type : Research Paper


Department of Statistics, Faculty of Administration and Economics, University of Al-Qadisyiah, Iraq


Quantile regression is a powerful statistical method for modeling and analyzing the impact of explanatory and response variables at different points in the conditional distribution of the response variable. Many research papers have indicated that Quantile Regression (QR) estimator is only resistant to vertical outliers. Quantile regression like other regression M-estimators and Least Absolute Deviation LAD can be very sensitive to outliers in explanatory variables (Leverage Points). To~overcome this drawback, at first, we have to use a robust, effective and efficient method to identify high leverage points if there is masking and swamping problems. In literature, the usage of Generalized M-estimator (GM-estimator) is proposed to estimate the unknown parameters against high leverage points. In this paper, we proposed weighted~method's the generalized- M for quantile regression namely  (GMQu), and improve the algorithm of this method by adapting the Improved Diagnostic Robust Generalized Potential (IDRGP) method. So that the calculation of the initial weights in this algorithm depends on (IDRGP), we're going to symbolize that method by (GMQuID). Simulation study and real data are considered to verify the performance of our proposed methods compared to other methods.


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Volume 13, Issue 2
July 2022
Pages 1325-1333
  • Receive Date: 08 November 2021
  • Revise Date: 20 December 2021
  • Accept Date: 02 January 2022