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Biometrika 1990 77(1):43-54;
© 1990 by Biometrika Trust
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Estimation of variance functions in assays with possibly unequal replication and nonnormal data

M. DAVIDIAN

Department of Statistics, North Carolina State University Raleigh, North Carolina 27695-8203, U.S.A.

Received for publication 1 February 1989. Revision received 1 June 1989.
  Abstract

Estimation of parametric variance functions using transformations of standard deviations based on replication at each design point is common in, but not limited to, assay analysis. It is shown that ignoring unequal replication can lead to bias and inefficiency in estimation. Efficiency comparisons for different transformations for nonnormal distributions are given. A method to account for bias is described that can offer robustness to nonnormality and leads to a comparison of Gini's mean difference to sample standard deviation. A method for computing all of these estimators using standard software is described.

Key Words: Efficiency • Gini's mean difference • Heteroscedasticity • Nonnormality • Prediction • Variance estimation


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