Kleffe, J.; Seifert, B. On the role of MINQUE in testing of hypotheses under mixed linear models. (English) Zbl 0655.62074 Commun. Stat., Theory Methods 17, No. 4, 1287-1309 (1988). From the summary: Testing of hypotheses under balanced ANOVA models is fairly simple and generally based on the usual ANOVA sums of squares. Difficulties may arise in special cases when these sums of squares do not form a complete sufficient statistic. There is a huge amount of literature on this subject, but there are only few results about unbalanced models. In such models the consideration of likelihood ratios leads to more complex sums of squares known from MINQUE theory. Uniform optimality of tests usually reduces to local optimality. Here we present a small review of methods proposed for testing hypotheses in unbalanced models, where MINQUE plays a major role. Cited in 5 Documents MSC: 62J10 Analysis of variance and covariance (ANOVA) Keywords:locally best invariant tests; mixed linear models; ANOVA-like tests; LBI-tests; asymptotic tests; level of significance; simulations; Satterthwaite approximation; two-way random model; ANOVA models; likelihood ratios; unbalanced models; MINQUE PDFBibTeX XMLCite \textit{J. Kleffe} and \textit{B. Seifert}, Commun. Stat., Theory Methods 17, No. 4, 1287--1309 (1988; Zbl 0655.62074) Full Text: DOI References: [1] Das R., Robust optimum invariant tests in one-way unbalanced and two-way balanced models (1986) [2] Humak, K.M.S. 1984. ”Statistische Methoden der Mo-dellbildung III”. Berlin: Akademie-Verlag. · Zbl 0556.62051 [3] DOI: 10.1214/aos/1176349663 · Zbl 0586.62078 · doi:10.1214/aos/1176349663 [4] DOI: 10.1002/bimj.4710220202 · Zbl 0459.62056 · doi:10.1002/bimj.4710220202 [5] Kleffe J., Linear Statistical Inference, Proc, Int. Conf. Paznan (1984) · Zbl 0577.62064 [6] Kleffe, J. and Rao, C.R. 1987. ”Estimation of variance components and applications”. North Holland Publishing Camp. · Zbl 0645.62073 [7] DOI: 10.1016/0047-259X(86)90062-X · Zbl 0583.62068 · doi:10.1016/0047-259X(86)90062-X [8] DOI: 10.1016/0047-259X(71)90001-7 · Zbl 0223.62086 · doi:10.1016/0047-259X(71)90001-7 [9] DOI: 10.1007/BF02288586 · Zbl 0063.06742 · doi:10.1007/BF02288586 [10] Schmidt W.H., Math. Operationsforsch. u. Statistics, Ser. Statistics 12 pp 243– (1981) [11] Seifert B., Math. Operationsforsch. u. Statistics. Ser. Statistics 10 pp 237– (1979) [12] Seifert B., Statistics 16 pp 621– (1985) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.