Some Modified Ridge Estimators for Handling the Multicollinearity Problem

Regression analysis is a statistical process that utilizes two or more predictor variables to predict a response variable. When the predictors included in the regression model are strongly correlated with each other, the problem of multicollinearity arises in the model. Due to this problem, the model variance increases significantly, leading to inconsistent ordinary least-squares estimators that may lead to invalid inferences. There are numerous existing strategies used to solve the multicollinearity issue, and one of the most used methods is ridge regression. The aim of this work is to develop novel estimators for the ridge parameter ? and compare them with existing estimators via extensive Monte Carlo simulation and real data sets based on the mean squared error criterion. The study findings indicate that the proposed estimators outperform the existing estimators.

Automated summary

Regression analysis is a statistical process that uses predictor variables to predict a response variable. Multicollinearity occurs when the predictors in the regression model are highly correlated with each other, leading to increased model variance and inconsistent estimators. Ridge regression is a commonly used method to solve the multicollinearity issue. This study aims to develop novel estimators for the ridge parameter and compare their performance with existing estimators using simulations and real data. The findings indicate that the proposed estimators outperform the existing ones.