Abstract
Optimal design of experiments for correlated processes is an increasingly relevant and active research topic. Present methods have restricted possibilities to judge their quality. To fill this gap, we complement the virtual noise approach by a convex formulation leading to an equivalence theorem comparable to the uncorrelated case and to an algorithm giving an upper performance bound against which alternative design methods can be judged. Moreover, a method for generating exact designs follows naturally. We exclusively consider estimation problems on a finite design space with a fixed number of elements. A comparison on some classical examples from the literature as well as a real application is provided.
Funding Statement
A. Pázman was supported by the Slovak VEGA grants No. 1/0341/19 and No. 1/0362/22. M. Hainy was supported by the Austrian Science Fund (FWF): J3959-N32. W.G. Müller was partially supported by project grants LIT-2017-4-SEE-001 funded by the Upper Austrian Government, and Austrian Science Fund (FWF): I 3903-N32.
Acknowledgments
We are most grateful for the helpful comments of two referees and an associate editor, which led to improvements in the paper.
Citation
Andrej Pázman. Markus Hainy. Werner G. Müller. "A convex approach to optimum design of experiments with correlated observations." Electron. J. Statist. 16 (2) 5659 - 5691, 2022. https://doi.org/10.1214/22-EJS2071
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