An equivalence theorem for design optimality with respect to a multi-objective criterion

Chiara Tommasi (), Juan M. Rodríguez-Díaz () and Jesús F. López-Fidalgo ()
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Chiara Tommasi: University of Milan
Juan M. Rodríguez-Díaz: University of Salamanca
Jesús F. López-Fidalgo: University of Navarre

Statistical Papers, 2023, vol. 64, issue 4, No 3, 1056 pages

Abstract: Abstract Maxi-min efficiency criteria are a kind of multi-objective criteria, since they enable us to take into consideration several tasks expressed by different component-wise criteria. However, they are difficult to manage because of their lack of differentiability. As a consequence, maxi-min efficiency designs are frequently built through heuristic and ad hoc algorithms, without the possibility of checking for their optimality. The main contribution of this study is to prove that the maxi-min efficiency optimality is equivalent to a Bayesian criterion, which is differentiable. In addition, we provide an analytic method to find the prior probability associated with a maxi-min efficient design, making feasible the application of the equivalence theorem. Two illustrative examples show how the proposed theory works.

Keywords: Equivalence theorem; Maxi-min optimal designs; Standardized criteria (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-023-01431-2

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