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On misspecification of the dispersion matrix in mixed linear models

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Abstract

The general mixed linear model can be written y = Xβ + Zu + e, where β is a vector of fixed effects, u is a vector of random effects and e is a vector of random errors. In this note, we mainly aim at investigating the general necessary and sufficient conditions under which the best linear unbiased estimator for \({\varvec \varrho}({\varvec l}, {\varvec m}) = {\varvec l}{\varvec '}{\varvec \beta}+{\varvec m}{\varvec '}{\varvec u}\) is also optimal under the misspecified model. In addition, we offer approximate conclusions in some special situations including a random regression model.

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Authors and Affiliations

  1. Department of Foundation Courses, Huai’an College of Information Technology, 223003, Huai’an, People’s Republic of China

    Jian-Ying Rong

  2. Department of Computing Science, Huaiyin Institute of Technology, 223003, Huai’an, People’s Republic of China

    Xu-Qing Liu

Authors
  1. Jian-Ying Rong
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  2. Xu-Qing Liu
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Correspondence to Jian-Ying Rong.

Additional information

This research was partially supported by Grants HGQ0637 and HGQN0725 from Huaiyin Institute of Technology. The second author was supported the “Green & Blue Project” Program for 2008 to Cultivate Young Core Instructors.

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Rong, JY., Liu, XQ. On misspecification of the dispersion matrix in mixed linear models. Stat Papers 51, 445–453 (2010). https://doi.org/10.1007/s00362-009-0213-0

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  • DOI: https://doi.org/10.1007/s00362-009-0213-0

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