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Locally D-optimal designs for heteroscedastic polynomial measurement error models

Author

Listed:
  • Min-Jue Zhang

    (Shanghai Normal University)

  • Rong-Xian Yue

    (Shanghai Normal University)

Abstract

This paper considers constructions of optimal designs for heteroscedastic polynomial measurement error models. Corresponding approximate design theory is developed by using corrected score function approach, which leads to non-concave optimisation problems. For the weighted polynomial measurement error model of degree p with some commonly used heteroscedastic structures, the upper bounds for the number of support points of locally D-optimal designs can be determined explicitly. A numerical example is given to show how heteroscedastic structures affect the optimal designs.

Suggested Citation

  • Min-Jue Zhang & Rong-Xian Yue, 2020. "Locally D-optimal designs for heteroscedastic polynomial measurement error models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 643-656, August.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:6:d:10.1007_s00184-019-00745-2
    DOI: 10.1007/s00184-019-00745-2
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    References listed on IDEAS

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    1. Carmelo Rodríguez & Isabel Ortiz & Ignacio Martínez, 2016. "A-optimal designs for heteroscedastic multifactor regression models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 757-771, February.
    2. Arturo Zavala & Heleno Bolfarine & Mário Castro, 2007. "Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 515-530, September.
    3. Wong, Weng Kee, 1995. "On the equivalence of D and G-optimal designs in heteroscedastic models," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 317-321, December.
    4. Holger Dette & Matthias Trampisch, 2012. "Optimal Designs for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1140-1151, September.
    5. M. Konstantinou & H. Dette, 2015. "Locally optimal designs for errors-in-variables models," Biometrika, Biometrika Trust, vol. 102(4), pages 951-958.
    6. Lei He & Rong-Xian Yue, 2017. "R-optimal designs for multi-factor models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 717-732, November.
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    Cited by:

    1. Min-Jue Zhang & Rong-Xian Yue, 2021. "Optimal designs for homoscedastic functional polynomial measurement error models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 485-501, September.

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