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Properties of h‐Likelihood Estimators in Clustered Data

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  • Lee Youngjo
  • Gwangsu Kim

Abstract

We study properties of the maximum h‐likelihood estimators for random effects in clustered data. To define optimality in random effects predictions, several foundational concepts of statistics such as likelihood, unbiasedness, consistency, confidence distribution and the Cramer–Rao lower bound are extended. Exact probability statements about interval estimators for random effects can be made asymptotically without a prior assumption. Using the binary‐matched pair example, we illustrated that the use of random effects recover information, leading to the boon on estimating treatment effects.

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  • Lee Youngjo & Gwangsu Kim, 2020. "Properties of h‐Likelihood Estimators in Clustered Data," International Statistical Review, International Statistical Institute, vol. 88(2), pages 380-395, August.
    • Handle: RePEc:bla:istatr:v:88:y:2020:i:2:p:380-395
    DOI: 10.1111/insr.12354
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    References listed on IDEAS

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    1. Yudi Pawitan & Youngjo Lee, 2017. "Wallet Game: Probability, Likelihood, and Extended Likelihood," The American Statistician, Taylor & Francis Journals, vol. 71(2), pages 120-122, April.
    2. 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.
    3. Youngjo Lee & Jan F. Bjørnstad, 2013. "Extended likelihood approach to large-scale multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 553-575, June.
    4. Renjun Ma & Bent Jørgensen, 2007. "Nested generalized linear mixed models: an orthodox best linear unbiased predictor approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 625-641, September.
    5. Patrick O. Perry, 2017. "Fast moment-based estimation for hierarchical models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 267-291, January.
    6. Lee, Youngjo & Oh, Hee-Seok, 2014. "A new sparse variable selection via random-effect model," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 89-99.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Wang, Zhanfeng & Noh, Maengseok & Lee, Youngjo & Shi, Jian Qing, 2021. "A general robust t-process regression model," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).

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