Robust designs for experiments with blocks

ABSTRACT

For experiments running in field plots or over time, the observations are often correlated due to spatial or serial correlation, which leads to correlated errors in a linear model analyzing the treatment means. Without knowing the exact correlation matrix of the errors, it is not possible to compute the generalized least-squares estimator for the treatment means and use it to construct optimal designs for the experiments. In this paper, we propose to use neighborhoods to model the covariance matrix of the errors, and apply a modified generalized least-squares estimator to construct robust designs for experiments with blocks. A minimax design criterion is investigated, and a simulated annealing algorithm is developed to find robust designs. We have derived several theoretical results, and representative examples are presented.

Keywords:

• Autocorrelation
• Block design
• Covariance neighborhood
• D-optimal design
• Generalized least-squares estimator
• Linear regression
• Minimax design
• Spatial correlation

Mathematics Subject Classification:

• 62K10
• 62K05

Acknowledgments

The authors are grateful to the Editor and referee for their helpful comments and suggestions.

Funding

This research was partially supported by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada.