Performance of Some Improved Estimators and their Robust Versions in Presence of Multicollinearity and Outliers

Nusrat Yasmin () and B. M. Golam Kibria ()
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Nusrat Yasmin: Florida International University
B. M. Golam Kibria: Florida International University

Sankhya B: The Indian Journal of Statistics, 2025, vol. 87, issue 1, No 8, 173-219

Abstract: Abstract The ridge regression estimator (RRE) is widely used as an improved estimator for estimating regression parameters in multicollinear linear regression models. However, an argument exists that in the presence of outliers, the dataset may adversely affect these improved estimators (Australian J. Stat. 33(3), 319–333, 1991). This paper proposes several improved estimators and their robust versions to address the multicollinearity problem, regardless of the presence of outliers. To evaluate these estimators, both Monte Carlo simulations and two real-life datasets were utilized, considering various outlier scenarios. We consider the smaller Mean Squared Error (MSE) value as a performance criterion. The simulation study demonstrates that when the dataset contains no outliers, the improved estimators generally outperform most of the robust versions, except for (RRE and RKL). However, in the presence of outliers, all the robust versions of these improved estimators perform better than all conventional improved estimators.

Keywords: Linear regression; Kibria-Lukman estimator; Mean square error; M-estimator; Multicollinearity; Outliers; Ridge regression; Simulation study; 62J05; 62J07; 62F10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13571-025-00352-4

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