Enhanced weighted least squares regression: A robust approach for managing outliers and heteroscedasticity
1 Department of Basic Sciences, Babcock University. Ilishan-Remo, Ogun State. Nigeria.
2 Department of Mathematical Sciences, Adeleke University, Ede, Osun State, Nigeria.
3 Department of Statistics University of Fort Hare Alice, Eastern Cape, South Africa.
4 Department of Statistics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State. Nigeria
Research Article
International Journal of Science and Technology Research Archive, 2024, 07(02), 097-106.
Article DOI: 10.53771/ijstra.2024.7.2.0064
Publication history:
Received on 04 October 2024; revised on 20 December 2024; accepted on 23 December 2024
Abstract:
The Ordinary Least Squares (OLS) approach performs best in the best-case scenario, but when the homoscedasticity and outlier-absence assumptions are broken, it performs noticeably worse. With an emphasis on Robust Weighted Least Squares (RWLS), M-estimation, and Least Trimmed Squares (LTS), this paper assesses robust alternatives to OLS. OLS was demonstrated to be extremely sensitive to outliers using a dataset on state-level crime rates in the US; the Mean Squared Error (MSE) increased from 5.480 (original data) to 12.580 (with outliers). On the other hand, RWLS using Tukey's Bisquare function produced the most consistent coefficient estimates and the smallest MSE, increasing from 4.520 to 5.340. In comparison to OLS, M-estimation and LTS also demonstrated lower MSE and higher resilience. The findings show how well robust approaches—in particular, RWLS with Tukey's Bisquare—address heteroscedasticity and outliers, which makes them essential for practical regression analysis.
Keywords:
Heteroscedasticity; Outliers; Robust regression; M-estimation; Tukey’s Bisquare
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Copyright © 2024 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0