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Optimal design of experiments via linear programming

Author

Listed:
  • Katarína Burclová

    (Comenius University Bratislava)

  • Andrej Pázman

    (Comenius University Bratislava)

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.

Suggested Citation

  • Katarína Burclová & Andrej Pázman, 2016. "Optimal design of experiments via linear programming," Statistical Papers, Springer, vol. 57(4), pages 893-910, December.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0782-7
    DOI: 10.1007/s00362-016-0782-7
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    References listed on IDEAS

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    1. Lenka Filová & Mária Trnovská & Radoslav Harman, 2012. "Computing maximin efficient experimental designs using the methods of semidefinite programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 709-719, July.
    2. Radoslav Harman, 2004. "Minimal efficiency of designs under the class of orthogonally invariant information criteria," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 137-153, September.
    3. Harman, Radoslav & Jurík, Tomás, 2008. "Computing c-optimal experimental designs using the simplex method of linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 247-254, December.
    Full references (including those not matched with items on IDEAS)

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