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Confidence distribution inferences in one-way random effects model

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  • Xuhua Liu
  • Xingzhong Xu

Abstract

In this paper, we construct a new kind of confidence intervals for the parameters of interest through constructing confidence distributions for them in one-way random effects model. At first, we use the method of Singh et al. (Ann Stat 33:159–183, 2005 ) to derive combined asymptotic confidence distribution, then obtain the confidence interval naturally by the property of confidence distribution. Simulation results demonstrate that the new confidence intervals perform very well in terms of empirical coverage probability and average interval length. Although we focus on confidence interval estimation, our method can also be used to carry out hypothesis tests about the parameters of interest. Copyright Sociedad de Estadística e Investigación Operativa 2016

Suggested Citation

  • Xuhua Liu & Xingzhong Xu, 2016. "Confidence distribution inferences in one-way random effects model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 59-74, March.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:1:p:59-74
    DOI: 10.1007/s11749-015-0440-8
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    References listed on IDEAS

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    1. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
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    6. 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.
    7. 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.
    8. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    9. Xie, Minge & Singh, Kesar & Strawderman, William E., 2011. "Confidence Distributions and a Unifying Framework for Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 320-333.
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    Cited by:

    1. Yuichi Goto & Koichi Arakaki & Yan Liu & Masanobu Taniguchi, 2023. "Homogeneity tests for one-way models with dependent errors under correlated groups," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 163-183, March.

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