Open Access
July, 1981 Optimum Balanced Block and Latin Square Designs for Correlated Observations
J. Kiefer, H. P. Wynn
Ann. Statist. 9(4): 737-757 (July, 1981). DOI: 10.1214/aos/1176345515

Abstract

In this paper designs are found which are optimum for various models that include some autocorrelation in the covariance structure $V$. First it is noted that the ordinary least squares estimator is quite robust against small perturbations in $V$ from the uncorrelated case $V_0 = \sigma^2_I$. This "local" argument justifies our use of such estimators and restriction to the class of designs $\mathscr{X}^\ast$ (balanced incomplete block or Latin squares) optimum under $V_0$. Within $\mathscr{X}^\ast$ we search for designs for which the least squares estimator minimizes appropriate functionals of the dispersion matrix under various correlation models $V$. In particular, we consider "nearest neighbor" correlation models in detail. The solutions lead to interesting combinatorial conditions somewhat similar to those encountered in "repeated measurement" designs. Typically, however, the latter need not be BIBD's and require twice as many blocks. For Latin squares, and hypercubes, the conditions are less restrictive than those giving "completeness."

Citation

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J. Kiefer. H. P. Wynn. "Optimum Balanced Block and Latin Square Designs for Correlated Observations." Ann. Statist. 9 (4) 737 - 757, July, 1981. https://doi.org/10.1214/aos/1176345515

Information

Published: July, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0546.62051
MathSciNet: MR624701
Digital Object Identifier: 10.1214/aos/1176345515

Subjects:
Primary: 62K05
Secondary: 05B20

Keywords: balanced incomplete block designs , correlated observations , difference sets , Latin squares and hypercubes , Optimum designs

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • July, 1981
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