Coverage-based performance of confidence intervals for linear regression coefficients under multicollinearity: Simulation and application

Year 2025, Early Access, 1 - 22

Sultana Mubarika Rahman Chowdhury , Zoran Bursac , B M Golam Kibria

https://doi.org/10.15672/hujms.1760551

Abstract

The shrinkage parameters in the ridge regression model have been extensively discussed and compared in the literature. Typically, the mean square error is used as the primary criterion for comparison. However, it does not fully explain the inferential performance of the estimator. This paper aims to examine 18 ridge regression regularization parameters based on their coverage probability and confidence interval widths using a simulation approach under various conditions. The results reveal that even though most estimators exhibit narrower confidence intervals compared to ordinary least squares, the shrinkage parameters that demonstrate a lower mean square error do not consistently maintain a coverage probability of 95. Additionally, increasing collinearity widens the width of the confidence interval. This paper studies the impact of multicollinearity on confidence interval coverage in linear regression models and provides information for researchers interested
in inference based on confidence intervals.

Keywords

Confidence interval , coverage probability , multicollinearity , multiple linear regression , ridge regression

References

• [1] M. M. Al-Kassab and M. Q. Al-Awjar, A Monte Carlo comparison between least squares and the new ridge regression parameters, J. Adv. Appl. Stat. 62 (1), 97-105, 2020.