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Minimax robust designs for regression models with heteroscedastic errors

Author

Listed:
  • Kai Yzenbrandt

    (University of Victoria)

  • Julie Zhou

    (University of Victoria)

Abstract

Minimax robust designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, we can show that the objective function of the minimax robust design problem is a difference of two convex functions. An effective algorithm is developed to compute minimax robust designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax robust designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax robust designs.

Suggested Citation

  • Kai Yzenbrandt & Julie Zhou, 2022. "Minimax robust designs for regression models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 203-222, February.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:2:d:10.1007_s00184-021-00827-0
    DOI: 10.1007/s00184-021-00827-0
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    References listed on IDEAS

    as
    1. Linglong Kong & Douglas P. Wiens, 2015. "Model-Robust Designs for Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 233-245, March.
    2. Weng Kee Wong & Yue Yin & Julie Zhou, 2019. "Using SeDuMi to find various optimal designs for regression models," Statistical Papers, Springer, vol. 60(5), pages 1583-1603, October.
    3. Holger Dette & Weng Kee Wong, 1999. "Optimal Designs When the Variance Is A Function of the Mean," Biometrics, The International Biometric Society, vol. 55(3), pages 925-929, September.
    4. Fei Yan & Chongqi Zhang & Heng Peng, 2017. "Optimal designs for additive mixture model with heteroscedastic errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6401-6411, July.
    Full references (including those not matched with items on IDEAS)

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