SOME ROBUST REGRESSION ESTIMATORS TO HANDLE OUTLIER AND HIGH DIMENSIONALITY IN LINEAR REGRESSION MODEL

Abstract

This study focuses on addressing the challenges of high dimensionality and outlier detection in linear regression models. With the proliferation of data collection technologies, big data analytics has become prominent, requiring efficient techniques to handle structured, semi-structured, and unstructured data. Traditional linear regression models are often limited in accommodating anomalies such as high dimensionality and outliers that commonly arise in modern datasets. In this research, the aim is on the performance of some robust estimators to handle both high dimensionality and outliers in the linear regression model. The methodology of the research consists of Robust Ridge Regression, Robust Principal Component Analysis, Robust Elastic Net, Least Absolute Shrinkage Selection Operator (LASSO), and Robust Stepwise Regression. The data was generated by conducting a Monte Carlo simulation experiment on a linear Regression Model. The result of the analysis was evaluated and compared using Root Mean Square Error (RMSE). Through a combination of real-life and simulated data, the research findings suggested that Robust Elastic Net estimators provided the most efficient estimator in terms of handling both high dimensionality and outliers. The results highlighted the superiority of the Robust Elastic Net estimator compared to other existing methods, showcasing their efficiency and effectiveness in mitigating the challenges associated with both outliers and high dimensionality in linear regression models.