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Optimale Zweifachblockpläne bei seriell korrelierten Fehlern. (German) Zbl 0542.62068
Summary: Williams-designs are proved to be optimal within the class of Latin 4\(\times 4\)-squares in row-column-models, where serial correlations are fitted with an autoregressive scheme of first order. Designs are presented that are not generalized Youden-designs and that are better than Williams-designs for strong negative correlations. However, it will be shown that optimal designs do not depend on the special structure of the error covariance in models with only two columns and in models with a completely symmetric covariance matrix.

MSC:
62K05 Optimal statistical designs
62K10 Statistical block designs
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References:
[1] Berenblut, I.I., undG.I. Webb: Experimental design in the presence of autocorrelated errors. Biometrika61, 1974, 427–437. · Zbl 0301.62044
[2] Budde, M.:D-optimale Versuchspläne für einfache lineare Modelle mit korrelierten Beobachtungen. Diplomarbeit, Universität Dortmund 1981.
[3] Cheng, C.-S., undC.-F. Wu: Balanced repeated measurements designs. Ann. Statist.8, 1980, 1272–1283. · Zbl 0461.62064
[4] Feld, M.: D-optimale Zeilen-Spaltenpläne für den Vergleich dreier Behandlungen. Diplomarbeit, Universität Dortmund 1981.
[5] Kiefer, J.: Construction and optimality of generalized Youden designs: In: A Survey of Stat. Designs and Linear Models. Amsterdam 1975. · Zbl 0313.62057
[6] Kiefer, J., undH.P. Wynn: Optimum balanced block and latin square designs for correlated observations. Ann. Statist.9, 1981, 737–757. · Zbl 0546.62051
[7] Krafft, O.: Lineare statistische Modelle und optimale Versuchspläne. Göttingen 1978. · Zbl 0386.62048
[8] Kunert, J.: Optimal design and refinement of the linear model with applications to repeated measurements design. Forschungsbericht 81/2, Universität Dortmund, 1981a. · Zbl 0522.62054
[9] Kunert, J.: Verallgemeinerungen von Sätzen von Cheng und Wu für Modelle mit Nachwirkungseffekten. Forschungsbericht 81/12, Universität Dortmund 1981b.
[10] Sonnemann, E.: D-optimality of complete latin squares. Erscheint in Math. Operationsforsch. Statistik, Ser. Statistics, 1978. · Zbl 0506.62058
[11] Sonnemann, E.: U-optimale Zeilen-Spaltenpläne für den Vergleich zweier Behandlungen. Erscheint in Metrika, 1979.
[12] Williams, E.J.: Experimental designs balanced for the estimation of residual effects of treatments. Austr.J.Sci.Res.A.2, 1949, 149–168.
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