Elfving’s theorem for R-optimality of experimental designs

Xin Liu and Rong-Xian Yue ()
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Xin Liu: Donghua University
Rong-Xian Yue: Shanghai Normal University

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 4, No 4, 485-498

Abstract: Abstract The present paper is devoted to the construction of R-optimal designs in multiresponse linear models. The R-optimality criterion introduced by Dette (J R Stat Soc Ser B 59:97–110, 1997) minimizes the volume of Bonferroni rectangular confidence region for the parameter estimation. A generalization of Elfving’s theorem is proved for the optimal designs with respect to R-optimality, which gives a geometric characterization of R-optimal designs. The geometric characterizations of the R-optimal designs are illustrated by four examples.

Keywords: Elfving set; Approximate design theory; Optimal design (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00184-019-00728-3

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