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Identical Predictions for Different Singular Mixed Models

  • Shiqing Wang
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 122)

Abstract

In linear mixed models theory one is assumed to know the structure of random effects covariance matrix. The suggestions are sometimes contradictious, especially if the model includes interactions between fixed effects and random effects. Mols [3] presented conditions under which two different random effects’ variance matrices will yield equal estimation and prediction results during the paper it is assumed that X is of full column rank. Wang [11] weakened the conditions of his theorem, and obtained the same results as his. Wang [12] extended Mols’s [3] results to situation that X is deficient in rank. Wang [13] gave a series of results it is assumed that X is possibly deficient in rank. They contain some necessary and sufficient theorems. We extend Wang’s [11-13] results to singular linear mixed models in this paper.

Keywords

linear mixed models best linear unbiased estimator best linear unbiased predictor robustly predictable mean square error 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shiqing Wang
    • 1
  1. 1.College of Mathematics and Information SciencesNorth China University of Water Resources and Electric PowerZhengzhouChina

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