New quantile based ridge M-estimator for linear regression models with multicollinearity and outliers. Issue 4 (3rd April 2023)

• Record Type: Journal Article
• Authors: Suhail, Muhammad; Chand, Sohail; Aslam, Muhammad
• Is Part Of: Communications in statistics. Volume 52:Issue 4(2023)
• Page Start: 1418
• Page End: 1435
• Publication Date: 2023-04-03
• Subjects: M-estimator -- Mean squared error -- Multicollinearity -- Outliers -- Ridge parameter -- Ridge regression -- Signal-to-noise ratio; 62J05 -- 62J07; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2021.1884715
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: The ordinary least squares and ridge regression estimators in a multiple linear regression model with multicollinearity and y -direction outliers lead to unfavorable results. In order to mitigate such situation, the available literature provides few ridge M-estimators to get precise estimates. The ridge parameter, k, plays a vital role in a bias-variance tradeoff for these estimators. However, for high signal-to-noise ratio and multicollinearity with y -direction outliers, the available methods may not perform well in terms of their mean squared error. In this article, we propose a new quantile based ridge M-estimator. The new estimator gives an automated choice of quantile probability of ridge parameter according to the level of noise and multicollinearity. Based on a simulation study, the new estimator outperforms the ordinary least square estimator, ridge estimator, and other considered ridge M-estimators especially for high multicollinearity, significant error variance, and y -direction outliers. Besides normal distribution, new estimator also performs well for heavy-tailed error distribution. Finally, two real-life examples are used to illustrate the application of the proposed estimator.