Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers

The violation of the assumption of homoscedasticity in OLS method, usually called heteroscedasticity, gravely misleads the inferential statistics. The current study has considered the situation when outliers occur in heteroscedastic data. Hence, the main focus of this research is to take remedial m...

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Main Author:	Rana, Md. Sohel
Format:	Thesis
Language:	English English
Published:	2010
Subjects:	Robust statistics Homoscedasticity Regression analysis - Mathematical models
Online Access:	http://psasir.upm.edu.my/id/eprint/19684/1/IPM_2010_5_F.pdf
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spelling	my-upm-ir.196842013-04-08T03:29:51Z Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers 2010-10 Rana, Md. Sohel The violation of the assumption of homoscedasticity in OLS method, usually called heteroscedasticity, gravely misleads the inferential statistics. The current study has considered the situation when outliers occur in heteroscedastic data. Hence, the main focus of this research is to take remedial measures on the violation of the assumption of homoscedasticity in the presence of outliers. This thesis also concerns on the normality assumption of the errors of regression model in the presence of outliers. It is now evident that outliers have great impact on the existing normality tests, heteroscedasticity tests, and the estimators for heteroscedastic model. We propose the Robust Rescaled Moment (RRM) test for testing the normality of the regression residuals when there is an evidence of outlier(s). The results of the study signify that the RRM test offers substantial improvements over other existing tests in the presence of outliers. For the detection of heteroscedasticity in the presence of outliers, a modified version of the classical Goldfeld-Quandt (MGQ) test is proposed which is most powerful than the classical tests of heteroscedasticity. Most statistics practitioners assume that the forms of the heteroscedastic error structures are known which may lead to inefficient estimates if it is not correctly specified. In this respect, a Leverage Based Near-Neighbor (LBNN) method is proposed, where prior information on the structure of the heteroscedastic error is not required. The findings indicate that the LBNN is very efficient for correcting the problem of heteroscedastic errors with unknown structure. We also examine the effect of outliers on the existing remedial measures of heteroscedasticity. Hence, in this thesis, a one step M-type of Robust Weighted Least Squares Method (RWLS) and the Two-Step Robust Weighted Least Squares (TSRWLS) are developed. Finally, the new robust wild bootstrap techniques which are resistant to outliers are proposed. The proposed techniques are based on the weighted residuals which incorporated the MM estimator, robust location, robust scale and the bootstrap sampling schemes of Wu (1986) and Liu (1988). All procedures, in this thesis, are examined by using real data and Monte Carlo simulation studies. The comparative studies among the classical and proposed robust methods reveal that all the proposed robust methods outperform the classical methods. Robust statistics Homoscedasticity Regression analysis - Mathematical models 2010-10 Thesis http://psasir.upm.edu.my/id/eprint/19684/ http://psasir.upm.edu.my/id/eprint/19684/1/IPM_2010_5_F.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Robust statistics Homoscedasticity Regression analysis - Mathematical models Institute for Mathematical Research English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Robust statistics Homoscedasticity Regression analysis - Mathematical models
spellingShingle	Robust statistics Homoscedasticity Regression analysis - Mathematical models Rana, Md. Sohel Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers
description	The violation of the assumption of homoscedasticity in OLS method, usually called heteroscedasticity, gravely misleads the inferential statistics. The current study has considered the situation when outliers occur in heteroscedastic data. Hence, the main focus of this research is to take remedial measures on the violation of the assumption of homoscedasticity in the presence of outliers. This thesis also concerns on the normality assumption of the errors of regression model in the presence of outliers. It is now evident that outliers have great impact on the existing normality tests, heteroscedasticity tests, and the estimators for heteroscedastic model. We propose the Robust Rescaled Moment (RRM) test for testing the normality of the regression residuals when there is an evidence of outlier(s). The results of the study signify that the RRM test offers substantial improvements over other existing tests in the presence of outliers. For the detection of heteroscedasticity in the presence of outliers, a modified version of the classical Goldfeld-Quandt (MGQ) test is proposed which is most powerful than the classical tests of heteroscedasticity. Most statistics practitioners assume that the forms of the heteroscedastic error structures are known which may lead to inefficient estimates if it is not correctly specified. In this respect, a Leverage Based Near-Neighbor (LBNN) method is proposed, where prior information on the structure of the heteroscedastic error is not required. The findings indicate that the LBNN is very efficient for correcting the problem of heteroscedastic errors with unknown structure. We also examine the effect of outliers on the existing remedial measures of heteroscedasticity. Hence, in this thesis, a one step M-type of Robust Weighted Least Squares Method (RWLS) and the Two-Step Robust Weighted Least Squares (TSRWLS) are developed. Finally, the new robust wild bootstrap techniques which are resistant to outliers are proposed. The proposed techniques are based on the weighted residuals which incorporated the MM estimator, robust location, robust scale and the bootstrap sampling schemes of Wu (1986) and Liu (1988). All procedures, in this thesis, are examined by using real data and Monte Carlo simulation studies. The comparative studies among the classical and proposed robust methods reveal that all the proposed robust methods outperform the classical methods.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Rana, Md. Sohel
author_facet	Rana, Md. Sohel
author_sort	Rana, Md. Sohel
title	Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers
title_short	Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers
title_full	Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers
title_fullStr	Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers
title_full_unstemmed	Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers
title_sort	robust diagnostics and estimation in heteroscedastic regression model in the presence of outliers
granting_institution	Universiti Putra Malaysia
granting_department	Institute for Mathematical Research
publishDate	2010
url	http://psasir.upm.edu.my/id/eprint/19684/1/IPM_2010_5_F.pdf
_version_	1747811442120196096

Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers

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