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A Comparison of Five Robust Regression Methods With Ordinary Least Squares Regression: Relative Efficiency, Bias, and Test of the Null Hypothesis.

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Title: A Comparison of Five Robust Regression Methods With Ordinary Least Squares Regression: Relative Efficiency, Bias, and Test of the Null Hypothesis.
Authors: Anderson, Cynthia, Schumacker, Randall E.
Source: Understanding Statistics. 2003, Vol. 2 Issue 2, p79. 25p.
Subject Terms: *Monte Carlo method, Regression analysis data processing, Least squares
Abstract: Monte Carlo simulations were used to generate data for a comparison of 5 robust regression estimation methods with ordinary least squares (OLS) under 36 different outlier data configurations. Two of the robust estimators, least absolute value (LAV) estimation and minimum m-estimation (MM), are available in certain statistical software packages. Three author-written variations of MM were included (MM 1, MM2, and MM3). Design parameters that were varied included sample size, number of independent predictor variables, outlier density, and outlier location. Criteria on which the regression methods were compared are relative efficiency, bias, and a test of the null hypothesis. Results indicated that MM2 was the best performing robust estimator on relative efficiency. The best performing estimator on bias was MM1. The best performing regression method on the test of the null hypothesis was MM2. Overall, the MM-type robust regression methods outperformed OLS and LAV on relative efficiency, bias, and the test of the null hypothesis. [ABSTRACT FROM AUTHOR]
Copyright of Understanding Statistics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Comparison of Five Robust Regression Methods With Ordinary Least Squares Regression: Relative Efficiency, Bias, and Test of the Null Hypothesis.
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  Data: Monte Carlo simulations were used to generate data for a comparison of 5 robust regression estimation methods with ordinary least squares (OLS) under 36 different outlier data configurations. Two of the robust estimators, least absolute value (LAV) estimation and minimum m-estimation (MM), are available in certain statistical software packages. Three author-written variations of MM were included (MM 1, MM2, and MM3). Design parameters that were varied included sample size, number of independent predictor variables, outlier density, and outlier location. Criteria on which the regression methods were compared are relative efficiency, bias, and a test of the null hypothesis. Results indicated that MM2 was the best performing robust estimator on relative efficiency. The best performing estimator on bias was MM1. The best performing regression method on the test of the null hypothesis was MM2. Overall, the MM-type robust regression methods outperformed OLS and LAV on relative efficiency, bias, and the test of the null hypothesis. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Understanding Statistics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1207/S15328031US0202_01
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        Text: English
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      – SubjectFull: Regression analysis data processing
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      – SubjectFull: Least squares
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      – TitleFull: A Comparison of Five Robust Regression Methods With Ordinary Least Squares Regression: Relative Efficiency, Bias, and Test of the Null Hypothesis.
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