A Simulation-Based Comparative Analysis of Two-Parameter Robust Ridge M-Estimators for Linear Regression Models

Bushra Haider, Syed Muhammad Asim, Danish Wasim and B. M. Golam Kibria ()
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Bushra Haider: Department of Statistics, University of Peshawar, Peshawar 25000, Pakistan
Syed Muhammad Asim: Department of Statistics, University of Peshawar, Peshawar 25000, Pakistan
Danish Wasim: Department of Statistics, Government Superior Science College Peshawar, Peshawar 25000, Pakistan
B. M. Golam Kibria: Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA

Stats, 2025, vol. 8, issue 4, 1-19

Abstract: Traditional regression estimators like Ordinary Least Squares (OLS) and classical ridge regression often fail under multicollinearity and outlier contamination respectively. Although recently developed two-parameter ridge regression (TPRR) estimators improve efficiency by introducing dual shrinkage parameters, they remain sensitive to extreme observations. This study develops a new class of Two-Parameter Robust Ridge M-Estimators (TPRRM) that integrate dual shrinkage with robust M-estimation to simultaneously address multicollinearity and outliers. A Monte Carlo simulation study, conducted under varying sample sizes, predictor dimensions, correlation levels, and contamination structures, compares the proposed estimators with OLS, ridge, and the most recent TPRR estimators. The results demonstrate that TPRRM consistently achieves the lowest Mean Squared Error (MSE), particularly in heavy-tailed and outlier-prone scenarios. Application to the Tobacco and Gasoline Consumption datasets further validates the superiority of the proposed methods in real-world conditions. The findings confirm that the proposed TPRRM fills a critical methodological gap by offering estimators that are not only efficient under multicollinearity, but also robust against departures from normality.

Keywords: MSE; OLS; ridge regression; robust ridge regression; simulation study; two-parameter estimator (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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