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On best linear unbiased estimation in the restricted general linear model. (English) Zbl 0613.62035
T. Mathew [Math. Operationsforsch. Stat., Ser. Stat. 14, 3-6 (1983; Zbl 0531.62061)] gave a necessary and sufficient condition for the BLUE of $$X\beta$$ under a general unrestricted linear model $$M=(y,X\beta,V)$$ to be also the BLUE of $$X\beta$$ under the corresponding restricted model $$M_ r=(y,X\beta |$$ $$R\beta =s,V)$$. In this note, Mathew’s result is supplemented by a necessary and sufficient condition for the BLUE of $$X\beta$$ under $$M_ r$$ to be also the BLUE of $$X\beta$$ under M. As a corollary, a necessary and sufficient condition is obtained for the two BLUE’s in question to be equal. This corollary shows that a result of J. K. Baksalary and R. Kala [ibid. 10, 27-35 (1979; Zbl 0416.62049)] can be interpreted to be correct, contrary to the claim of Mathew.

##### MSC:
 62F10 Point estimation 62J05 Linear regression; mixed models 62J99 Linear inference, regression
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##### References:
 [1] Baksalary J.K., Math. Operationsforsch. Statist., ser. statist. 10 pp 27– (1979) [2] DOI: 10.1080/03081087408817070 · doi:10.1080/03081087408817070 [3] Mathew T., Math. Operationsforsch. Statist. ser. statist. 14 pp 3– (1983) [4] Rao C.R., Sankhya Ser. A 33 pp 371– (1971) [5] Rao C.R., Generalized Inverse of Matrices and its Applications (1971) · Zbl 0236.15004
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