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Inferences About Two-Parameter Multicollinear Gaussian Linear Regression Models: An Empirical Type I Error and Power Comparison

Author

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  • Md Ariful Hoque

    (Department of Biostatistics, Florida International University, Miami, FL 33199, USA)

  • Zoran Bursac

    (Department of Biostatistics, Florida International University, Miami, FL 33199, USA)

  • B. M. Golam Kibria

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

Abstract

In linear regression analysis, the independence assumption is crucial and the ordinary least square (OLS) estimator generally regarded as the Best Linear Unbiased Estimator (BLUE) is applied. However, multicollinearity can complicate the estimation of the effect of individual variables, leading to potential inaccurate statistical inferences. Because of this issue, different types of two-parameter estimators have been explored. This paper compares t -tests for assessing the significance of regression coefficients, including several two-parameter estimators. We conduct a Monte Carlo study to evaluate these methods by examining their empirical type I error and power characteristics, based on established protocols. The simulation results indicate that some two-parameter estimators achieve better power gains while preserving the nominal size at 5%. Real-life data are analyzed to illustrate the findings of this paper.

Suggested Citation

  • Md Ariful Hoque & Zoran Bursac & B. M. Golam Kibria, 2025. "Inferences About Two-Parameter Multicollinear Gaussian Linear Regression Models: An Empirical Type I Error and Power Comparison," Stats, MDPI, vol. 8(2), pages 1-34, April.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:2:p:28-:d:1640782
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    References listed on IDEAS

    as
    1. Issam Dawoud & B. M. Golam Kibria, 2020. "A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model," Stats, MDPI, vol. 3(4), pages 1-16, November.
    2. Mustafa I. Alheety & HM Nayem & B. M. Golam Kibria, 2025. "An Unbiased Convex Estimator Depending on Prior Information for the Classical Linear Regression Model," Stats, MDPI, vol. 8(1), pages 1-33, February.
    3. 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.
    4. Ashok V. Dorugade, 2014. "A Modified Two-Parameter Estimator in Linear Regression," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(1), pages 23-36, January.
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