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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Format: | Thesis |
Language: | en_US |
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Summary: | 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. |
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