Skip to main content
SpringerLink
Log in

Optimale Zweifachblockpläne bei Seriell Korrelierten Fehlern

  • Publication
  • Published:
Metrika Aims and scope Submit manuscript

Summary

Williams-designs are proved to be optimal within the class of latin 4×4-squares in rowcolumn-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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literaturverzeichnis

  • Berenblut, I.I., undG.I. Webb: Experimental design in the presence of autocorrelated errors. Biometrika61, 1974, 427–437.

    Article  MathSciNet  MATH  Google Scholar 

  • Budde, M.:D-optimale Versuchspläne für einfache lineare Modelle mit korrelierten Beobachtungen. Diplomarbeit, Universität Dortmund 1981.

  • Cheng, C.-S., undC.-F. Wu: Balanced repeated measurements designs. Ann. Statist.8, 1980, 1272–1283.

    Article  MathSciNet  MATH  Google Scholar 

  • Feld, M.: D-optimale Zeilen-Spaltenpläne für den Vergleich dreier Behandlungen. Diplomarbeit, Universität Dortmund 1981.

  • Kiefer, J.: Construction and optimality of generalized Youden designs: In: A Survey of Stat. Designs and Linear Models. Amsterdam 1975.

  • Kiefer, J., undH.P. Wynn: Optimum balanced block and latin square designs for correlated observations. Ann. Statist.9, 1981, 737–757.

    Article  MathSciNet  MATH  Google Scholar 

  • Krafft, O.: Lineare statistische Modelle und optimale Versuchspläne. Göttingen 1978.

  • Kunert, J.: Optimal design and refinement of the linear model with applications to repeated measurements design. Forschungsbericht 81/2, Universität Dortmund, 1981a.

  • Kunert, J.: Verallgemeinerungen von Sätzen von Cheng und Wu für Modelle mit Nachwirkungseffekten. Forschungsbericht 81/12, Universität Dortmund 1981b.

  • Sonnemann, E.: D-optimality of complete latin squares. Erscheint in Math. Operationsforsch. Statistik, Ser. Statistics, 1978.

  • Sonnemann, E.: U-optimale Zeilen-Spaltenpläne für den Vergleich zweier Behandlungen. Erscheint in Metrika, 1979.

  • Williams, E.J.: Experimental designs balanced for the estimation of residual effects of treatments. Austr.J.Sci.Res.A.2, 1949, 149–168.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung Statistik der Universität, Postfach 50 05 00, D4600, Dortmund 50

    M. Budde

Authors
  1. M. Budde
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Budde, M. Optimale Zweifachblockpläne bei Seriell Korrelierten Fehlern. Metrika 31, 203–213 (1984). https://doi.org/10.1007/BF01915201

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01915201

Search

Navigation