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Some equalities for estimations of variance components in a general linear model and its restricted and transformed models


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  • Tian, Yongge
  • Liu, Chunmei


For the unknown positive parameter [sigma]2 in a general linear model , the two commonly used estimations are the simple estimator (SE) and the minimum norm quadratic unbiased estimator (MINQUE). In this paper, we derive necessary and sufficient conditions for the equivalence of the SEs and MINQUEs of the variance component [sigma]2 in the original model [physics M-matrix (script capital m)], the restricted model , the transformed model , and the misspecified model .

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 101 (2010)
Issue (Month): 9 (October)
Pages: 1959-1969

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Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:1959-1969

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Keywords: Linear regression model Restricted model Transformed model Sub-sample model Reduced model Simple estimator Minimum norm quadratic unbiased estimator Equality for estimators Matrix rank method;


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Cited by:
  1. Yuqin Sun & Rong Ke & Yongge Tian, 2014. "Some overall properties of seemingly unrelated regression models," AStA Advances in Statistical Analysis, Springer, vol. 98(2), pages 103-120, April.


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