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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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Vol. 57; no. 4; pp. 893 - 910
Main Authors: Burclova, Katarina, Pazman, Andrej
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2016
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-016-0782-7