Quantile-based robust Kibria–Lukman estimator for linear regression model to combat multicollinearity and outliers: Real life applications using T20 cricket sports and anthropometric data

• Published in: Kuwait journal of science 2025-01, Vol.52 (1), p.100336, Article 100336
• Main Authors: Wasim, Danish, Suhail, Muhammad, Khan, Sajjad Ahmad, Shabbir, Maha, Awwad, Fuad A., Ismail, Emad A.A., Ahmad, Hijaz, Ali, Amjad
• Format: Article
• Language: English
• Subjects: Mean squared error; Multicollinearity; Ordinary least squares; Outliers; Quantile-based robust ridge regression; Ridge regression
• ISSN: 2307-4108
• DOI: 10.1016/j.kjs.2024.100336

The performance of ordinary least squares (OLS) and ridge regression (RR) are influenced when outliers are present in y-direction with multicollinearity among independent variables. The robust RR with ridge parameters provides a biased estimator that has a smaller variance than conventional OLS and RR estimators. The optimal value of the ridge parameter has a vital role in bias-variance tradeoff. This study proposes quantile-based estimation of ridge parameter in robust RR to deal with the joint issue of y-direction outliers and multicollinearity. The effectiveness of the proposed estimators is evaluated using intensive Monte Carlo simulation and two real data sets in terms of mean square error (MSE) and predictions sum of squared error (PSSE) criterion. Simulation findings reveal that the newly developed estimators of ridge parameter in robust RR have better performance than OLS, RR, and existing robust RR estimators when errors are normally and non-normally distributed. The results from two numerical examples of T20 Cricket sports and anthropometric data show that the new estimator with quantile probability 0.50 and 0.99 respectively has winning performance among all competing and proposed estimators. •Multicollinearity and outliers pose challenges in linear regression models.•A new robust ridge M-estimator addresses multicollinearity with y-direction outliers.•The proposed estimators efficiently handle multicollinearity with dependent variable outliers.•Simulations and real data show the effectiveness of the proposed ridge estimators.