Abstract
It is shown that comparison of linear models with singular covariance matrices may be reduced to the same problem for non-singular covariance matrices. Moreover the problem of linearly sufficient statistics, considered by Drygas (1983) is reduced to comparison of linear models.
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Baksalary JK, Kala R (1981) Linear transformations preserving best linear unbiased estimators in a general Gauss-Markoff model. Ann Statist 9:913–916
Drygas H (1983) Sufficiency and completeness in the general Gauss-Markov model. Sankhyā A 45: 88–98
Ehrenfeld S (1955) Complete class theorem in experimental design. Proc 3rd Berkeley Symp Math Statist Prob 1:69–75
Hansen OH, Torgersen EN (1974) Comparison of linear normal experiments. Ann Statist 2:367–373
LaMotte LR (1977) A canonical form for general linear model. Ann Statist 5:787–789
Rao CR (1973) Linear statistical inference and its applications, 2nd ed. Wiley, New York
Stępniak C (1983) Optimal allocation of units in experimental designs with hierarchical and cross classification. Ann Inst Statist Math A 35:461–473
Stępniak C (1985) Ordering of nonnegative definite matrices with application to comparison of linear models. Linear Algebra Appl 70:67–71
Stępniak C, Torgersen E (1981) Comparison of linear models with partially known covariances with respect to unbiased estimation. Scand J Statist 8:183–184
Stępniak C, Wang SG, Wu CFJ (1984) Comparison of linear experiments with known covariances. Ann Statist 12:35–365
Torgersen EN (1976) Comparison of statistical experiments. Scand J Statist 3:186–208
Torgersen E (1984) Orderings of linear models. J Statist Plann and Inference 9:1–17
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Stępniak, C. Reduction problems in comparison of linear models. Metrika 34, 211–216 (1987). https://doi.org/10.1007/BF02613151
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DOI: https://doi.org/10.1007/BF02613151