A robust rescaled moment test for normality in regression
Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Science Publications
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/12852/ http://psasir.upm.edu.my/id/eprint/12852/1/A%20robust%20rescaled%20moment%20test%20for%20normality%20in%20regression.pdf |
| _version_ | 1848841949129211904 |
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| author | Rana, Md. Sohel Midi, Habshah Imon, A. H. M. Rahmatulah |
| author_facet | Rana, Md. Sohel Midi, Habshah Imon, A. H. M. Rahmatulah |
| author_sort | Rana, Md. Sohel |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study showed that normality tests suffer huge set back in the presence of outliers. We proposed a new robust omnibus test based on rescaled moments and coefficients of skewness and kurtosis of residuals that we call robust rescaled moment test. Results: Numericalexamples and Monte Carlo simulations showed that this proposed test performs better than the existingtests for normality in the presence of outliers. Conclusion/Recommendation: We recommend using ourproposed omnibus test instead of the existing tests for checking the normality of the regressionresiduals. |
| first_indexed | 2025-11-15T07:51:21Z |
| format | Article |
| id | upm-12852 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:51:21Z |
| publishDate | 2009 |
| publisher | Science Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-128522015-10-30T01:47:29Z http://psasir.upm.edu.my/id/eprint/12852/ A robust rescaled moment test for normality in regression Rana, Md. Sohel Midi, Habshah Imon, A. H. M. Rahmatulah Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study showed that normality tests suffer huge set back in the presence of outliers. We proposed a new robust omnibus test based on rescaled moments and coefficients of skewness and kurtosis of residuals that we call robust rescaled moment test. Results: Numericalexamples and Monte Carlo simulations showed that this proposed test performs better than the existingtests for normality in the presence of outliers. Conclusion/Recommendation: We recommend using ourproposed omnibus test instead of the existing tests for checking the normality of the regressionresiduals. Science Publications 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12852/1/A%20robust%20rescaled%20moment%20test%20for%20normality%20in%20regression.pdf Rana, Md. Sohel and Midi, Habshah and Imon, A. H. M. Rahmatulah (2009) A robust rescaled moment test for normality in regression. Journal of Mathematics and Statistics, 5 (1). pp. 54-62. ISSN 1549-3644; ESSN: 1558-6359 http://thescipub.com/abstract/10.3844/jmssp.2009.54.62 10.3844/jmssp.2009.54.62 |
| spellingShingle | Rana, Md. Sohel Midi, Habshah Imon, A. H. M. Rahmatulah A robust rescaled moment test for normality in regression |
| title | A robust rescaled moment test for normality in regression |
| title_full | A robust rescaled moment test for normality in regression |
| title_fullStr | A robust rescaled moment test for normality in regression |
| title_full_unstemmed | A robust rescaled moment test for normality in regression |
| title_short | A robust rescaled moment test for normality in regression |
| title_sort | robust rescaled moment test for normality in regression |
| url | http://psasir.upm.edu.my/id/eprint/12852/ http://psasir.upm.edu.my/id/eprint/12852/ http://psasir.upm.edu.my/id/eprint/12852/ http://psasir.upm.edu.my/id/eprint/12852/1/A%20robust%20rescaled%20moment%20test%20for%20normality%20in%20regression.pdf |