Minimax robust designs for field experiments |
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Authors: | Beiyan Ou Julie Zhou |
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Institution: | (1) Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada, V8W 3P4 |
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Abstract: | Experimental designs for field experiments are useful in planning agricultural experiments, environmental studies, etc. Optimal
designs depend on the spatial correlation structures of field plots. Without knowing the correlation structures exactly in
practice, we can study robust designs. Various neighborhoods of covariance matrices are introduced and discussed. Minimax
robust design criteria are proposed, and useful results are derived. The generalized least squares estimator is often more
efficient than the least squares estimator if the spatial correlation structure belongs to a small neighborhood of a covariance
matrix. Examples are given to compare robust designs with optimal designs.
The work was partially supported by research grants from the Natural Science and Engineering Research Council of Canada. |
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Keywords: | Check variety Covariance neighborhood Generalized least squares Minimax design Optimal design Spatial correlation |
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