Optimal design of experiments via linear programming

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 -optimal designs in a linear regression model are reformulated here as “infinite-dimensional”...

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Vydané v:	Statistical papers (Berlin, Germany) Ročník 57; číslo 4; s. 893 - 910
Hlavní autori:	Burclova, Katarina, Pazman, Andrej
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2016 Springer Nature B.V
Predmet:	Approximation Computation Design of experiments Design optimization Economic Theory/Quantitative Economics/Mathematical Methods Economics Eigenvalues Finance Inequality Insurance Linear programming Management Mathematical functions Mathematical models Mathematics and Statistics Operations Research/Decision Theory Optimality criteria Optimization Probability Theory and Stochastic Processes Regression Regression analysis Regular Article Statistics Statistics for Business Studies Texts Regression models 62J05 Concave maximization 62K05 Relaxation method Criterion-robust design Optimality criteria
ISSN:	0932-5026, 1613-9798
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Popis
Shrnutí:	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 -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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ISSN:	0932-5026 1613-9798
DOI:	10.1007/s00362-016-0782-7