Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems
In the multiple linear regression analysis, the ridge regression estimator is often used to address the problem of multicollinearity. Besides multicollinearity, outliers also constitute a problem in the multiple linear regression analysis. We propose a new biased estimators of the robust ridge regre...
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The Canadian Center of Science and Education
2015
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my.utm.605142021-08-19T03:37:13Z http://eprints.utm.my/id/eprint/60514/ Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems Pati, Kafi Dano Adnan, Robiah Rasheed, Bello Abdulkadir QA Mathematics In the multiple linear regression analysis, the ridge regression estimator is often used to address the problem of multicollinearity. Besides multicollinearity, outliers also constitute a problem in the multiple linear regression analysis. We propose a new biased estimators of the robust ridge regression called the Ridge Least Median Squares (RLMS) estimator in the presence of multicollinearity and outliers. For this purpose, a simulation study is conducted in order to see the difference between the proposed method and the existing methods in terms of their effectiveness measured by the mean square error. In our simulation studies the performance of the proposed method RLMS is examined for different number of observations and the different percentage of outliers. The results of different illustrative cases are presented. This paper also provides the results of the RLMS on a real-life data set. The results show that RLMS is better than the existing methods of Ordinary Least Squares (OLS), Ridge Least Absolute Value (RLAV) and Ridge Regression (RR) in the presence of multicollinearity and outliers. The Canadian Center of Science and Education 2015 Article PeerReviewed Pati, Kafi Dano and Adnan, Robiah and Rasheed, Bello Abdulkadir (2015) Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems. Modern Applied Science, 9 (2). pp. 191-198. ISSN 1913-1852 https://www.ccsenet.org/journal/index.php/mas/article/view/44146 |
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QA Mathematics Pati, Kafi Dano Adnan, Robiah Rasheed, Bello Abdulkadir Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems |
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In the multiple linear regression analysis, the ridge regression estimator is often used to address the problem of multicollinearity. Besides multicollinearity, outliers also constitute a problem in the multiple linear regression analysis. We propose a new biased estimators of the robust ridge regression called the Ridge Least Median Squares (RLMS) estimator in the presence of multicollinearity and outliers. For this purpose, a simulation study is conducted in order to see the difference between the proposed method and the existing methods in terms of their effectiveness measured by the mean square error. In our simulation studies the performance of the proposed method RLMS is examined for different number of observations and the different percentage of outliers. The results of different illustrative cases are presented. This paper also provides the results of the RLMS on a real-life data set. The results show that RLMS is better than the existing methods of Ordinary Least Squares (OLS), Ridge Least Absolute Value (RLAV) and Ridge Regression (RR) in the presence of multicollinearity and outliers. |
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Article |
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Pati, Kafi Dano Adnan, Robiah Rasheed, Bello Abdulkadir |
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Pati, Kafi Dano Adnan, Robiah Rasheed, Bello Abdulkadir |
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Pati, Kafi Dano |
title |
Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems |
title_short |
Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems |
title_full |
Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems |
title_fullStr |
Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems |
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Using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems |
title_sort |
using ridge least median squares to estimate the parameter by solving multicollinearity and outliers problems |
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The Canadian Center of Science and Education |
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2015 |
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http://eprints.utm.my/id/eprint/60514/ https://www.ccsenet.org/journal/index.php/mas/article/view/44146 |
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