The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad

Partial Least Squares regression (PLSR) is a regression technique that is commonly used to analyse the relationship between variables in high dimensional data. PLSR also offers good solution to multicollinearity problem in regression analysis. Hence, PLSR is a very powerful tool in dealing with mult...

Full description

Saved in:

Bibliographic Details
Main Author:	Mohamad, Mazni
Format:	Thesis
Language:	English
Published:	2021
Subjects:	Multivariate analysis Cluster analysis Longitudinal method
Online Access:	https://ir.uitm.edu.my/id/eprint/53591/1/53591.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-uitm-ir.53591
record_format	uketd_dc
spelling	my-uitm-ir.535912024-05-28T08:27:37Z The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad 2021-02 Mohamad, Mazni Multivariate analysis. Cluster analysis. Longitudinal method Regression analysis. Correlation analysis. Spatial analysis (Statistics) Partial Least Squares regression (PLSR) is a regression technique that is commonly used to analyse the relationship between variables in high dimensional data. PLSR also offers good solution to multicollinearity problem in regression analysis. Hence, PLSR is a very powerful tool in dealing with multivariate data especially that of high dimension. Multivariate data is however often contains outliers. The presence of outliers in a data set may cause the regression parameter estimates become imprecise; hence, lead us to making such an invalid conclusion. Several robust PLSR methods have been proposed by researchers to cater this outlying problem. One of those is known as Partial Robust M-regression (PRM). This method is very much emphasizes on the robust starting values and the weights to be used. Reason for such emphasis is to ensure that more protection can be given against both vertical outliers and high leverage points. This study focuses on the enhancement of PRM method by introducing several PRM-based methods. Altogether there are five PRM-based methods that have been proposed in this research which are Winsorized Mean PRM- based method (PRMWM), Tukey Bisquare PRM-based method (PRMBS), Hampel PRM-based method (PRMH), the integrated Winsorized Mean and Tukey Bisquare PRM-based method (PRMWMBS) and the integrated Winsorized Mean and Hampel method (PRMWMH). The performances of all methods are assessed through both numerical examples and simulation studies under various outlying conditions. In most conditions, the PRMWM, PRMBS and PRMH outperform the original PRM. However, the integrated approach seems not to be a good idea as the two methods proposed in this study which are PRMWMBS and PRMWMH are not performing well compared to PRM. In short, this study perceives that PRMWM is the best method among all proposed methods because it consistently outperforms other methods. In order to further assess the performance of the methods, this study introduced a new bootstrap method for regression models with high dimensional data which is Weighted Split Sample Bootstrap (WSSB). The accuracy of this bootstrap technique has been measured and compared to that of the Split Sample Bootstrap (SSB). Results indicate that WSSB outperforms SSB. Therefore, WSSB is then used to compare the performance of PRMWM as compared to PRM via numerical examples and simulation studies. In general, it can be seen that PRMWM outperforms other methods as it produces the smallest prediction error values. the same time, the establishment of these models can fill the gap in Islamic derivative study and promote the growth of Islamic financial products. 2021-02 Thesis https://ir.uitm.edu.my/id/eprint/53591/ https://ir.uitm.edu.my/id/eprint/53591/1/53591.pdf text en public phd doctoral Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences Mohamed Ramli, Norazan (Dr.)
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Mohamed Ramli, Norazan (Dr.)
topic	Multivariate analysis Cluster analysis Longitudinal method Multivariate analysis Cluster analysis Longitudinal method
spellingShingle	Multivariate analysis Cluster analysis Longitudinal method Multivariate analysis Cluster analysis Longitudinal method Mohamad, Mazni The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad
description	Partial Least Squares regression (PLSR) is a regression technique that is commonly used to analyse the relationship between variables in high dimensional data. PLSR also offers good solution to multicollinearity problem in regression analysis. Hence, PLSR is a very powerful tool in dealing with multivariate data especially that of high dimension. Multivariate data is however often contains outliers. The presence of outliers in a data set may cause the regression parameter estimates become imprecise; hence, lead us to making such an invalid conclusion. Several robust PLSR methods have been proposed by researchers to cater this outlying problem. One of those is known as Partial Robust M-regression (PRM). This method is very much emphasizes on the robust starting values and the weights to be used. Reason for such emphasis is to ensure that more protection can be given against both vertical outliers and high leverage points. This study focuses on the enhancement of PRM method by introducing several PRM-based methods. Altogether there are five PRM-based methods that have been proposed in this research which are Winsorized Mean PRM- based method (PRMWM), Tukey Bisquare PRM-based method (PRMBS), Hampel PRM-based method (PRMH), the integrated Winsorized Mean and Tukey Bisquare PRM-based method (PRMWMBS) and the integrated Winsorized Mean and Hampel method (PRMWMH). The performances of all methods are assessed through both numerical examples and simulation studies under various outlying conditions. In most conditions, the PRMWM, PRMBS and PRMH outperform the original PRM. However, the integrated approach seems not to be a good idea as the two methods proposed in this study which are PRMWMBS and PRMWMH are not performing well compared to PRM. In short, this study perceives that PRMWM is the best method among all proposed methods because it consistently outperforms other methods. In order to further assess the performance of the methods, this study introduced a new bootstrap method for regression models with high dimensional data which is Weighted Split Sample Bootstrap (WSSB). The accuracy of this bootstrap technique has been measured and compared to that of the Split Sample Bootstrap (SSB). Results indicate that WSSB outperforms SSB. Therefore, WSSB is then used to compare the performance of PRMWM as compared to PRM via numerical examples and simulation studies. In general, it can be seen that PRMWM outperforms other methods as it produces the smallest prediction error values. the same time, the establishment of these models can fill the gap in Islamic derivative study and promote the growth of Islamic financial products.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mohamad, Mazni
author_facet	Mohamad, Mazni
author_sort	Mohamad, Mazni
title	The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad
title_short	The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad
title_full	The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad
title_fullStr	The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad
title_full_unstemmed	The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad
title_sort	enhancement of partial robust m-regression (prm) and split sample bootstrap (ssb) for high dimensional data with outliers / mazni mohamad
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2021
url	https://ir.uitm.edu.my/id/eprint/53591/1/53591.pdf
_version_	1804889638505021440

The enhancement of partial robust m-regression (PRM) and split sample bootstrap (SSB) for high dimensional data with outliers / Mazni Mohamad

Similar Items