A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data

The Ordinary Least Square (OLS) is a widely used method of estimation in classical regression analysis to investigate the linear relationship among the variables of interest. The OLS estimator is the Best Linear Unbiased Estimator (BLUE) when the two assumptions are fulfilled: i) independency of exp...

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Main Author:	Nur Aqilah Binti Ferdaos
Format:	Thesis
Language:	en_US
Subjects:	Regression analysis > Asymptotic theory Least squares Estimation theory
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spelling	my-usim-ddms-125192024-05-29T04:15:38Z A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data Nur Aqilah Binti Ferdaos The Ordinary Least Square (OLS) is a widely used method of estimation in classical regression analysis to investigate the linear relationship among the variables of interest. The OLS estimator is the Best Linear Unbiased Estimator (BLUE) when the two assumptions are fulfilled: i) independency of explanatory variables and ii) normality of error distribution. However, these assumptions are invalid in the presence of multicollinearity and outliers. The term multicollinearity refers to high dependency among the explanatory variables while outlier is an observation that is very peculiar from the entire observed data. The well-known ridge regression method is unable to overcome the multicollinearity problem in the presence of outliers. The presence of outliers will pull the fitted lines towards it and result in poor and unreliable parameter estimates. This study proposes a combination method of estimation of Generalized Mestimators (GM) and ridge parameter (k) or known as GM-estimator with k = k* that is robust towards both multicollinearity and outliers with the selected proposed robust estimates. The performance of the proposed method was discussed and compared via Monte Carlo simulation studies. The proposed estimator yielded unbiased estimates with small Mean Square Error (MSE) in the presence of multicollinearity and outliers in the data. The simulation results indicated that the proposed method produced a reliable parameter estimates that is robust towards both problems. Finally, the performance of the proposed method was tested using two real datasets that were contaminated with both multicollinearity and outliers: i) the relationship between stock market price and macroeconomic variables in Malaysia and ii) Maryland Crime Rates. The empirical results showed that the proposed method GM-estimator with k = k* was able to outperform other existing methods towards multicollinearity and outliers in real data problem. Universiti Sains Islam Malaysia 2018-04 Thesis en_US https://oarep.usim.edu.my/handle/123456789/12519 https://oarep.usim.edu.my/bitstreams/cc1df9eb-6873-4364-9ff6-8d4c5b64c4ac/download 8a4605be74aa9ea9d79846c1fba20a33 Regression analysis -- Asymptotic theory Least squares Estimation theory
institution	Universiti Sains Islam Malaysia
collection	USIM Institutional Repository
language	en_US
topic	Regression analysis -- Asymptotic theory Least squares Estimation theory
spellingShingle	Regression analysis -- Asymptotic theory Least squares Estimation theory Nur Aqilah Binti Ferdaos A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data
description	The Ordinary Least Square (OLS) is a widely used method of estimation in classical regression analysis to investigate the linear relationship among the variables of interest. The OLS estimator is the Best Linear Unbiased Estimator (BLUE) when the two assumptions are fulfilled: i) independency of explanatory variables and ii) normality of error distribution. However, these assumptions are invalid in the presence of multicollinearity and outliers. The term multicollinearity refers to high dependency among the explanatory variables while outlier is an observation that is very peculiar from the entire observed data. The well-known ridge regression method is unable to overcome the multicollinearity problem in the presence of outliers. The presence of outliers will pull the fitted lines towards it and result in poor and unreliable parameter estimates. This study proposes a combination method of estimation of Generalized Mestimators (GM) and ridge parameter (k) or known as GM-estimator with k = k* that is robust towards both multicollinearity and outliers with the selected proposed robust estimates. The performance of the proposed method was discussed and compared via Monte Carlo simulation studies. The proposed estimator yielded unbiased estimates with small Mean Square Error (MSE) in the presence of multicollinearity and outliers in the data. The simulation results indicated that the proposed method produced a reliable parameter estimates that is robust towards both problems. Finally, the performance of the proposed method was tested using two real datasets that were contaminated with both multicollinearity and outliers: i) the relationship between stock market price and macroeconomic variables in Malaysia and ii) Maryland Crime Rates. The empirical results showed that the proposed method GM-estimator with k = k* was able to outperform other existing methods towards multicollinearity and outliers in real data problem.
format	Thesis
author	Nur Aqilah Binti Ferdaos
author_facet	Nur Aqilah Binti Ferdaos
author_sort	Nur Aqilah Binti Ferdaos
title	A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data
title_short	A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data
title_full	A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data
title_fullStr	A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data
title_full_unstemmed	A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data
title_sort	robust ridge regression for multicollinearity problem in the presence of outliers in the data
granting_institution	Universiti Sains Islam Malaysia
_version_	1812444873145450496

A Robust Ridge Regression For Multicollinearity Problem In The Presence Of Outliers In The Data

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