Cover Image

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...

Full description

Saved in:
Bibliographic Details
Main Author: Rana, Md. Sohel
Format: Thesis
Language:English
English
Published: 2010
Online Access:http://psasir.upm.edu.my/id/eprint/19684/1/IPM_2010_5_F.pdf
http://psasir.upm.edu.my/id/eprint/19684/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.19684
record_format eprints
spelling my.upm.eprints.196842013-04-08T03:29:51Z http://psasir.upm.edu.my/id/eprint/19684/ Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers 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. 2010-10 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/19684/1/IPM_2010_5_F.pdf Rana, Md. Sohel (2010) Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers. PhD thesis, Universiti Putra Malaysia. English
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
English
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
author Rana, Md. Sohel
spellingShingle Rana, Md. Sohel
Robust Diagnostics and Estimation in Heteroscedastic Regression Model in the Presence of Outliers
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
publishDate 2010
url http://psasir.upm.edu.my/id/eprint/19684/1/IPM_2010_5_F.pdf
http://psasir.upm.edu.my/id/eprint/19684/
_version_ 1643827112466972672
score 13.251813

Similar Items