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

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 multicollinear...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2024-11, Vol.53 (11), p.5442-5452
Main Authors: Shabbir, Maha, Chand, Sohail, Iqbal, Farhat
Format: Article
Language:English
Subjects:
Collinearity
Error analysis
Estimators
Heteroscedastic or autocorrelated
Monte Carlo simulations
MSE
Multicollinearity
Parameter estimation
Regression models
Ridge regression
Standard error
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Summary: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.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2023.2186874