The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors
The Ordinary Least Squares (OLS) method is the most popular technique in statistics and is often use to estimate the parameters of a model because of tradition and ease of computation. The OLS provides an efficient and unbiased estimates of the parameters when the underlying assumptions, especiall...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
World Scientific and Engineering Academy and Society
2009
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/17266/ http://psasir.upm.edu.my/id/eprint/17266/1/The%20performance%20of%20robust%20weighted%20least%20squares%20in%20the%20presence%20of%20outliers%20and%20heteroscedastic%20errors.pdf |
| _version_ | 1848843194173751296 |
|---|---|
| author | Midi, Habshah Rana, Md. Sohel Imon, A. H. M. Rahmatullah |
| author_facet | Midi, Habshah Rana, Md. Sohel Imon, A. H. M. Rahmatullah |
| author_sort | Midi, Habshah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The Ordinary Least Squares (OLS) method is the most popular technique in statistics and is often use
to estimate the parameters of a model because of tradition and ease of computation. The OLS provides an
efficient and unbiased estimates of the parameters when the underlying assumptions, especially the assumption
of contant error variances (homoscedasticity), are satisfied. Nonetheless, in real situation it is difficult to retain
the error variance homogeneous for many practical reasons and thus there arises the problem of
heteroscedasticity. We generally apply the Weighted Least Squares (WLS) procedure to estimate the regression
parameters when heteroscedasticity occurs in the data. Nevertheless, there is evidence that the WLS estimators
suffer a huge set back in the presence of a few atypical observations that we often call outliers. In this situation
the analysis will become more complicated. In this paper we have proposed a robust procedure for the
estimation of regression parameters in the situation where heteroscedasticity comes together with the existence
of outliers. Here we have employed robust techniques twice, once in estimating the group variances and again in
determining weights for the least squares. We call this method Robust Weighted Least Squares (RWLS). The
performance of the newly proposed method is investigated extensively by real data sets and Monte Carlo
Simulations. The results suggest that the RWLS method offers substantial improvements over the existing
methods. |
| first_indexed | 2025-11-15T08:11:09Z |
| format | Article |
| id | upm-17266 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:11:09Z |
| publishDate | 2009 |
| publisher | World Scientific and Engineering Academy and Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-172662016-07-22T03:17:58Z http://psasir.upm.edu.my/id/eprint/17266/ The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors Midi, Habshah Rana, Md. Sohel Imon, A. H. M. Rahmatullah The Ordinary Least Squares (OLS) method is the most popular technique in statistics and is often use to estimate the parameters of a model because of tradition and ease of computation. The OLS provides an efficient and unbiased estimates of the parameters when the underlying assumptions, especially the assumption of contant error variances (homoscedasticity), are satisfied. Nonetheless, in real situation it is difficult to retain the error variance homogeneous for many practical reasons and thus there arises the problem of heteroscedasticity. We generally apply the Weighted Least Squares (WLS) procedure to estimate the regression parameters when heteroscedasticity occurs in the data. Nevertheless, there is evidence that the WLS estimators suffer a huge set back in the presence of a few atypical observations that we often call outliers. In this situation the analysis will become more complicated. In this paper we have proposed a robust procedure for the estimation of regression parameters in the situation where heteroscedasticity comes together with the existence of outliers. Here we have employed robust techniques twice, once in estimating the group variances and again in determining weights for the least squares. We call this method Robust Weighted Least Squares (RWLS). The performance of the newly proposed method is investigated extensively by real data sets and Monte Carlo Simulations. The results suggest that the RWLS method offers substantial improvements over the existing methods. World Scientific and Engineering Academy and Society 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17266/1/The%20performance%20of%20robust%20weighted%20least%20squares%20in%20the%20presence%20of%20outliers%20and%20heteroscedastic%20errors.pdf Midi, Habshah and Rana, Md. Sohel and Imon, A. H. M. Rahmatullah (2009) The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors. WSEAS Transactions on Mathematics, 8 (7). pp. 351-361. ISSN 1109-2769 http://www.wseas.us/e-library/transactions/mathematics/2009/29-388.pdf Least squares Error analysis (Mathematics) Robust statistics |
| spellingShingle | Least squares Error analysis (Mathematics) Robust statistics Midi, Habshah Rana, Md. Sohel Imon, A. H. M. Rahmatullah The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors |
| title | The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors |
| title_full | The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors |
| title_fullStr | The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors |
| title_full_unstemmed | The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors |
| title_short | The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors |
| title_sort | performance of robust weighted least squares in the presence of outliers and heteroscedastic errors |
| topic | Least squares Error analysis (Mathematics) Robust statistics |
| url | http://psasir.upm.edu.my/id/eprint/17266/ http://psasir.upm.edu.my/id/eprint/17266/ http://psasir.upm.edu.my/id/eprint/17266/1/The%20performance%20of%20robust%20weighted%20least%20squares%20in%20the%20presence%20of%20outliers%20and%20heteroscedastic%20errors.pdf |