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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/11375

Title: Ordinary Least Squares and Robust Estimators in Linear Regression: Impacts of Outliers, Error and Response Contaminations
Authors: Adedia, David
Adebanji, Atinuke
Labeodan, Moremi
Adeyemi, Shola
Keywords: Ordinary least squares estimator
Robust estimators
Power of the test
Issue Date: 2016
Publisher: British Journal of Mathematics & Computer Science
Citation: British Journal of Mathematics & Computer Science 13(4): 1-11, 2016, Article no.BJMCS.22876
Abstract: The Ordinary Least Squares Estimator (OLSE) is the best method for linear regression if the classical assumptions are satis ed for estimating weights. When these assumptions are violated, the robust methods give more reliable estimates while the OLSE is strongly a ected adversely. In order to assess the sensitivity of some estimators using more than ve criteria, a secondary dataset on Anthropometric measurements from Komfo Anokye Teaching Hospital, Kumasi-Ghana, is used. In this study, we compare the performance of the Huber Maximum Likelihood Estimator (HMLE), Least Trimmed Squares Estimator (LTSE), S Estimator (SE) and Modi ed Maximum Likelihood Estimator (MMLE) relative to the OLSE when the dataset has normal errors; 10, 20 and 30 percent outliers; 20% error contamination and lognormal contamination in the response variable. In the assessment, we use coe cients and their standard errors, relative e ciencies, Root Mean Square Errors, and the coe cients of determination of the estimators. We also use the power of the test to assess the e ects of the aberrations on the post hoc power analysis of the estimators. The results show the SE and MMLE outperform the HMLE and LTSE while the OLSE breaks down completely. The LTSE performs well when the trimming is done to eliminate only the outliers. Also, SE and MMLE resist the e ect of all aberrations in the data and also have good post hoc power analysis.
Description: An article published by British Journal of Mathematics & Computer Science 13(4): 1-11, 2016, Article no.BJMCS.22876
URI: http://hdl.handle.net/123456789/11375
Appears in Collections:College of Science

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