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On unbiasedness of the empirical BLUE and BLUP

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  • Jiang, Jiming

Abstract

Let y = X[beta] + Z[alpha] + [epsilon] be a mixed linear model, where [beta] is a vector of fixed effects, [alpha] is a vector of random effects, and [epsilon] is a vector of errors. Kackar and Harville (1984) showed that the best linear unbiased estimator (BLUE) of [beta] and the best linear unbiased predictor (BLUP) of [alpha] remain unbiased if the true variance components at which the BLUE and BLUP are computed are replaced by nonnegative, even and translation-invariant estimators, provided the expectations of the resulting empirical BLUE and BLUP exist. In this short note, we show that when there is a single random effect factor in the model, those expectations do exist.

Suggested Citation

  • Jiang, Jiming, 1999. "On unbiasedness of the empirical BLUE and BLUP," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 19-24, January.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:1:p:19-24
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    Cited by:

    1. Juvêncio S. Nobre & Julio M. Singer, 2011. "Leverage analysis for linear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1063-1072, February.
    2. Elff, Martin & Heisig, Jan Paul & Schaeffer, Merlin & Shikano, Susumu, 2021. "Rejoinder to Daniel Stegmueller's Comments," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 51(1), pages 460-462.
    3. Ranjbar, Setareh & Salvati, Nicola & Pacini, Barbara, 2023. "Estimating heterogeneous causal effects in observational studies using small area predictors," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).

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