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T‐optimum designs for discrimination between two multiresponse dynamic models

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  • Dariusz Uciński
  • Barbara Bogacka

Abstract

Summary. The paper is concerned with a problem of finding an optimum experimental design for discriminating between two rival multiresponse models. The criterion of optimality that we use is based on the sum of squares of deviations between the models and picks up the design points for which the divergence is maximum. An important part of our criterion is an additional vector of experimental conditions, which may affect the design. We give the necessary conditions for the design and the additional parameters of the experiment to be optimum, we present the algorithm for the numerical optimization procedure and we show the relevance of these methods to dynamic systems, especially to chemical kinetic models.

Suggested Citation

  • Dariusz Uciński & Barbara Bogacka, 2005. "T‐optimum designs for discrimination between two multiresponse dynamic models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 3-18, February.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:1:p:3-18
    DOI: 10.1111/j.1467-9868.2005.00485.x
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    Cited by:

    1. David Mogalle & Philipp Seufert & Jan Schwientek & Michael Bortz & Karl-Heinz Küfer, 2024. "Computing T-optimal designs via nested semi-infinite programming and twofold adaptive discretization," Computational Statistics, Springer, vol. 39(5), pages 2451-2478, July.
    2. Ray-Bing Chen & Ping-Yang Chen & Cheng-Lin Hsu & Weng Kee Wong, 2020. "Hybrid algorithms for generating optimal designs for discriminating multiple nonlinear models under various error distributional assumptions," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-30, October.
    3. Laura Deldossi & Silvia Angela Osmetti & Chiara Tommasi, 2019. "Optimal design to discriminate between rival copula models for a bivariate binary response," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 147-165, March.
    4. Elisa Perrone & Andreas Rappold & Werner G. Müller, 2017. "$$D_s$$ D s -optimality in copula models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 403-418, August.
    5. Patan, Maciej & Bogacka, Barbara, 2007. "Optimum experimental designs for dynamic systems in the presence of correlated errors," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5644-5661, August.
    6. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2017. "T-optimal discriminating designs for Fourier regression models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 196-206.
    7. Dette, Holger & Titoff, Stefanie, 2008. "Optimal discrimination designs," Technical Reports 2008,06, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    8. Kira Alhorn & Holger Dette & Kirsten Schorning, 2021. "Optimal Designs for Model Averaging in non-nested Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 745-778, August.
    9. Duarte, Belmiro P.M. & Wong, Weng Kee & Atkinson, Anthony C., 2015. "A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 11-24.
    10. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.

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