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An exact upper limit for the variance bias in the carry-over model with correlated errors

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  • Sailer, Oliver

Abstract

The analysis of crossover designs assuming i.i.d. errors leads to biased variance estimates whenever the true covariance structure is not spherical. As a result, the OLS F-Test for treatment differences is not valid. Bellavance et al. (Biometrics 52:607-612, 1996) use simulations to show that a modified F-Test based on an estimate of the within subjects covariance matrix allows for nearly unbiased tests. Kunert and Utzig (JRSS B 55:919-927, 1993) propose an alternative test that does not need an estimate of the covariance matrix. However, for designs with more than three observations per subject Kunert and Utzig (1993) only give a rough upper bound for the worst-case variance bias. This may lead to overly conservative tests. In this paper we derive an exact upper limit for the variance bias due to carry-over for an arbitrary number of observations per subject. The result holds for a certain class of highly efficient carry-over balanced designs.

Suggested Citation

  • Sailer, Oliver, 2009. "An exact upper limit for the variance bias in the carry-over model with correlated errors," Technical Reports 2009,01, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200901
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