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Comparison of confidence intervals for variance components in an unbalanced one-way random effects model

Author

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  • Jiratampradab Arisa

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

  • Supapakorn Thidaporn

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

  • Suntornchost Jiraphan

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

Abstract

The purpose of this paper is to study and compare the methods for constructing confidence intervals for variance components in an unbalanced one-way random effects model. The methods are based on a classical exact, generalised pivotal quantity, a fiducial inference and a fiducial generalised pivotal quantity. The comparison of criteria involves the empirical coverage probability that maintains at the nominal confidence level of 0.95 and the shortest average length of the confidence interval. The simulation results show that the method based on the generalised pivotal quantity and the fiducial inference perform very well in terms of both the empirical coverage probability and the average length of the confidence interval. The classical exact method performs well in some situations, while the fiducial generalised pivotal quantity performs well in a very unbalanced design. Therefore, the method based on the generalised pivotal quantity is recommended for all situations.

Suggested Citation

  • Jiratampradab Arisa & Supapakorn Thidaporn & Suntornchost Jiraphan, 2022. "Comparison of confidence intervals for variance components in an unbalanced one-way random effects model," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 149-160, December.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:4:p:149-160:n:6
    DOI: 10.2478/stattrans-2022-0047
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Ting, Naitee & Burdick, Richard K. & Graybill, Franklin A. & Gui, Rongde, 1989. "One-sided confidence intervals on nonnegative sums of variance components," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 129-135, June.
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