Optimal design of experiments via linear programming

Katarína Burclová () and Andrej Pázman ()
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Katarína Burclová: Comenius University Bratislava
Andrej Pázman: Comenius University Bratislava

Statistical Papers, 2016, vol. 57, issue 4, No 3, 893-910

Abstract: Abstract We investigate the possibility of extending some results of Pázman and Pronzato (Ann Stat 42(4):1426–1451, 2014) to a larger set of optimality criteria. Namely, the problems of computing D-, A-, and $$E_k$$ E k -optimal designs in a linear regression model are reformulated here as “infinite-dimensional” linear programming problems. The same approach is applied to combination of these optimality criteria and to the “criterion robust” problem of Harman (Metrika 60:137–153, 2004). Approximate optimum designs can then be computed by a relaxation method (Shimizu and Aiyoshi in IEEE Trans Autom Control 25(1):62–66, 1980), and this is illustrated on various examples.

Keywords: Regression models; Optimality criteria; Concave maximization; Relaxation method; Criterion-robust design; 62K05; 62J05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00362-016-0782-7

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