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An optimal experimental design criterion for discriminating between non‐normal models

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  • J. López‐Fidalgo
  • C. Tommasi
  • P. C. Trandafir

Abstract

Summary. Typically T‐optimality is used to obtain optimal designs to discriminate between homoscedastic models with normally distributed observations. Some extensions of this criterion have been made for the heteroscedastic case and binary response models in the literature. In this paper, a new criterion based on the Kullback–Leibler distance is proposed to discriminate between rival models with non‐normally distributed observations. The criterion is coherent with the approaches mentioned above. An equivalence theorem is provided for this criterion and an algorithm to compute optimal designs is developed. The criterion is applied to discriminate between the popular Michaelis–Menten model and a typical extension of it under the log‐normal and the gamma distributions.

Suggested Citation

  • J. López‐Fidalgo & C. Tommasi & P. C. Trandafir, 2007. "An optimal experimental design criterion for discriminating between non‐normal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 231-242, April.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:2:p:231-242
    DOI: 10.1111/j.1467-9868.2007.00586.x
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    References listed on IDEAS

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    1. Jesus LOPEZ FIDALGO & Chiara TOMMASI & Paula Camelia TRANDAFIR, 2004. "T-optimality: a stopping rule for a first order algorithm," Departmental Working Papers 2004-30, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
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    Cited by:

    1. Santiago Campos-Barreiro & Jesús López-Fidalgo, 2015. "D-optimal experimental designs for a growth model applied to a Holstein-Friesian dairy farm," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 491-505, September.
    2. Woods, David C. & McGree, James M. & Lewis, Susan M., 2017. "Model selection via Bayesian information capacity designs for generalised linear models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 226-238.
    3. Elham Yousefi & Luc Pronzato & Markus Hainy & Werner G. Müller & Henry P. Wynn, 2023. "Discrimination between Gaussian process models: active learning and static constructions," Statistical Papers, Springer, vol. 64(4), pages 1275-1304, August.
    4. Rivas-López, M.J. & Yu, R.C. & López-Fidalgo, J. & Ruiz, G., 2017. "Optimal experimental design on the loading frequency for a probabilistic fatigue model for plain and fibre-reinforced concrete," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 363-374.
    5. 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.
    6. 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.
    7. S. G. J. Senarathne & C. C. Drovandi & J. M. McGree, 2020. "Bayesian sequential design for Copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 454-478, June.
    8. 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.
    9. Víctor Casero-Alonso & Andrey Pepelyshev & Weng K. Wong, 2018. "A web-based tool for designing experimental studies to detect hormesis and estimate the threshold dose," Statistical Papers, Springer, vol. 59(4), pages 1307-1324, December.
    10. Dette, Holger & Titoff, Stefanie, 2008. "Optimal discrimination designs," Technical Reports 2008,06, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. Tommasi, C. & López-Fidalgo, J., 2010. "Bayesian optimum designs for discriminating between models with any distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 143-150, January.
    12. Jun Yu & HaiYing Wang, 2022. "Subdata selection algorithm for linear model discrimination," Statistical Papers, Springer, vol. 63(6), pages 1883-1906, December.
    13. 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.
    14. 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.

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