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Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model

Author

Listed:
  • Arisa Jiratampradab

    (Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

  • Jiraphan Suntornchost

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Thidaporn Supapakorn

    (Department of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand)

Abstract

The objective of this work is to propose the iteratively reweighted least squares concept to form a fiducial generalized pivotal quantity of the between-group variance component for the unbalanced variance components model. The fiducial generalized pivotal quantity is a subclass of the generalized pivotal quantity which is useful technique to deal with problem of nuisance parameters for finding interval estimator. This research provides the probability distribution and the properties of the statistics to lead the constructing of the confidence interval. The authors also prove the construction of the fiducial generalized pivotal quantity through iteratively reweighted least squares. The performance comparison for the new proposed method with other competing methods in the literature is studied through a simulation study. The results of the simulation study demonstrate that the proposed method is very satisfactory in terms of both the coverage probability and the average width of the confidence interval. Furthermore, the analysis of real data for patients of sickle cell disease also illustrates that the proposed method gives the smallest average width of the confidence interval. All these results confirm that the iteratively reweighted least squares fiducial generalized pivotal quantity confidence interval is recommended.

Suggested Citation

  • Arisa Jiratampradab & Jiraphan Suntornchost & Thidaporn Supapakorn, 2025. "Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model," Mathematics, MDPI, vol. 13(1), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:153-:d:1559643
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    References listed on IDEAS

    as
    1. Lidong, E. & Hannig, Jan & Iyer, Hari, 2008. "Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 854-865, June.
    2. Hartung, Joachim & Knapp, Guido, 2000. "Confidence intervals for the between group variance in the unbalanced one-way random effects model of analysis of variance," Technical Reports 2000,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Han, Jeongseop & Lee, Youngjo, 2024. "Enhanced Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    4. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    Full references (including those not matched with items on IDEAS)

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