A new ridge estimator for linear regression model with some challenging behavior of error term

Abstract

Ridge regression is a variant of linear regression that aims to circumvent the issue of collinearity among predictors. The ridge parameter $k$ has an important role in the bias-variance tradeoff. In this article, we introduce a new approach to select the ridge parameter to deal with the multicollinearity problem with different behavior of the error term. The proposed ridge estimator is a function of the number of predictors and the standard error of the regression model. An extensive simulation study is conducted to assess the performance of the estimators for the linear regression model with different error terms, which include normally distributed, non-normal and heteroscedastic or autocorrelated errors. Based upon the criterion of mean square error (MSE), it is found that the new proposed estimator outperforms OLS, commonly used and closely related estimators. Further, the application of the proposed estimator is provided on the COVID-19 data of India.

Keywords:

• Heteroscedastic or autocorrelated
• Monte Carlo simulations
• MSE
• Multicollinearity
• Ridge regression

Acknowledgment

The authors are thankful to the anonymous reviewer and the editor for their valuable comments and suggestions, which certainly improved the quality of the article.