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

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 d...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2023-08, Vol.64 (4), p.1041-1056
Main Authors: Tommasi, Chiara, Rodríguez-Díaz, Juan M., López-Fidalgo, Jesús F.
Format: Article
Language:English
Subjects:
Algorithms
Conditional probability
Criteria
Design optimization
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Efficiency
Equivalence
Finance
Insurance
Management
Mathematics and Statistics
Operations Research/Decision Theory
Parameter estimation
Probability Theory and Stochastic Processes
Regular Article
Statistics
Statistics for Business
Theorems
Citations: Items that this one cites
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Summary: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.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-023-01431-2