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Simultaneous optimality of LSE and ANOVA estimate in general mixed models

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Abstract

Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered. A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance (Hendreson III’s) estimate of variance components being uniformly minimum variance unbiased estimates simultaneously. This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest, and for finding equivalences of several common estimates of variance components.

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100022, P. R. China

    Mi Xia Wu & Song Gui Wang

  2. Division of Epidemiology, Statistics and Prevention Research, National Institute of Child Health and Human Development, NIH/DHHS, 6100 Executive Boulevard, Rockville, MD, 20852, USA

    Mi Xia Wu & Kai Fun Yu

Authors
  1. Mi Xia Wu
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  2. Song Gui Wang
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  3. Kai Fun Yu
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Correspondence to Mi Xia Wu.

Additional information

The work is supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality PHR (IHLB), National Natural Science Foundation of China (NSFC) (10801005) and (NSFC) (10771010) and the Intramural Research Program of the National Institute of Child Health and Human Development, National Institute of Health

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Wu, M.X., Wang, S.G. & Yu, K.F. Simultaneous optimality of LSE and ANOVA estimate in general mixed models. Acta. Math. Sin.-English Ser. 24, 1637–1650 (2008). https://doi.org/10.1007/s10114-008-6220-6

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  • DOI: https://doi.org/10.1007/s10114-008-6220-6

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