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Criteria for the equality between ordinay least squares and best linear unbiased estimators under certain linear models. (English) Zbl 0645.62072
Summary: A new necessary and sufficient condition is derived for the equality between the ordinary least-squares estimator and the best linear unbiased estimator of the expectation vector in linear models with certain specific design matrices. This condition is then applied to special cases involving one-way and two-way classification models.

62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
Full Text: DOI
[1] Alalouf, Topics in Applied Statistics pp 331– (1983)
[2] Baksalary, On equalities between BLUEs, WLSEs, and SLSEs, Canad. J. Statist. 11 pp 119– (1983) · Zbl 0522.62047
[3] Feuerverger, Categorical information and the singular linear model. Canad, J. Statist. 8 pp 41– (1980) · Zbl 0464.62060
[4] Pederzoli, Remarks on the equality of minimum variance unbiased estimators under two different models, Statistica (Bologna) 35 pp 791– (1975)
[5] Puntanen, S. (1987). On the relative goodness of ordinary least squares estimation in the general linear model. Acta Univ. Tamper. Ser. A, 216. · Zbl 0652.62050
[6] Puntanen, S., and Styan, G. P. H. (1988). On the equality of the ordinary least squares estimator and the best linear unbiased estimator. Amer. Statist., to appear.
[7] Rao, Least squares theory using an estimated dispersion matrix and its application to measurement of signals pp 355– (1967) · Zbl 0189.18503
[8] Rao, Unified theory of linear estimation, Sankhya Ser. A 33 pp 371– (1971) · Zbl 0236.62048
[9] Rao, Linear Statistical Inference and Its Applications (1973)
[10] Styan, Encyclopedia of Statistical Sciences, Volume 3: Fa √† di Bruno’s Formula to Hypothesis Testing pp 334– (1983)
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