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On Some Test Statistics for Testing the Regression Coefficients in Presence of Multicollinearity: A Simulation Study

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  • Sergio Perez-Melo

    (Department of Mathematics and Statistics, Florida International University, University Park, Miami, FL 33199, USA)

  • B. M. Golam Kibria

    (Department of Mathematics and Statistics, Florida International University, University Park, Miami, FL 33199, USA)

Abstract

Ridge regression is a popular method to solve the multicollinearity problem for both linear and non-linear regression models. This paper studied forty different ridge regression t -type tests of the individual coefficients of a linear regression model. A simulation study was conducted to evaluate the performance of the proposed tests with respect to their empirical sizes and powers under different settings. Our simulation results demonstrated that many of the proposed tests have type I error rates close to the 5% nominal level and, among those, all tests except one have considerable gain in powers over the standard ordinary least squares (OLS) t -type test. It was observed from our simulation results that seven tests based on some ridge estimators performed better than the rest in terms of achieving higher power gains while maintaining a 5% nominal size.

Suggested Citation

  • Sergio Perez-Melo & B. M. Golam Kibria, 2020. "On Some Test Statistics for Testing the Regression Coefficients in Presence of Multicollinearity: A Simulation Study," Stats, MDPI, vol. 3(1), pages 1-16, March.
    • Handle: RePEc:gam:jstats:v:3:y:2020:i:1:p:5-55:d:330743
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    References listed on IDEAS

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    1. R. Fallah & M. Arashi & S. M. M. Tabatabaey, 2017. "On the ridge regression estimator with sub-space restriction," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(23), pages 11854-11865, December.
    2. M. Norouzirad & M. Arashi, 2019. "Preliminary test and Stein-type shrinkage ridge estimators in robust regression," Statistical Papers, Springer, vol. 60(6), pages 1849-1882, December.
    3. Roozbeh, M. & Arashi, M., 2013. "Feasible ridge estimator in partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 35-44.
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    2. Jinse Jacob & R. Varadharajan, 2023. "Simultaneous raise regression: a novel approach to combating collinearity in linear regression models," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(5), pages 4365-4386, October.
    3. Muhammad Nadir Shabbir & Muhammad Usman Arshad & Muhammad Amir Alvi & Kainat Iftikhar, 2022. "Impact of Trade Policy Uncertainty and Sustainable Development on Medical Innovation for Developed Countries: An Application of DID Approach," Sustainability, MDPI, vol. 15(1), pages 1-26, December.
    4. Muhammad Nadir Shabbir & Wang Liyong & Muhammad Usman Arshad, 2022. "Trade Policy Uncertainty and Medical Innovation: Evidence from Developing Nations," Economies, MDPI, vol. 10(9), pages 1-23, September.

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