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Two competing linear random-effects models and their connections

Author

Listed:
  • Changli Lu

    (Shanghai Maritime University)

  • Yuqin Sun

    (Shanghai Maritime University)

  • Yongge Tian

    (Central University of Finance and Economics)

Abstract

Assume that an observed random vector is represented in two alternative linear random-effects models (LRMs). In this case, the results of statistical inference under the two LRMs are not necessarily the same. The objective of this paper is to study the performance of the best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) of all unknown parameters in two LRMs under most general assumptions on the covariance matrices of the random-effects terms and error terms. We establish necessary and sufficient conditions for the BLUPs/BLUEs to be equivalent under the two LRMs using some well-known formulas for calculating ranks of matrices and their generalized inverses, and also present various consequences and conclusions on some special special cases of LRMs.

Suggested Citation

  • Changli Lu & Yuqin Sun & Yongge Tian, 2018. "Two competing linear random-effects models and their connections," Statistical Papers, Springer, vol. 59(3), pages 1101-1115, September.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0806-3
    DOI: 10.1007/s00362-016-0806-3
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    References listed on IDEAS

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