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D-optimal designs based on the second-order least squares estimator

Author

Listed:
  • Lucy L. Gao

    (University of Victoria)

  • Julie Zhou

    (University of Victoria)

Abstract

When the error distribution in a regression model is asymmetric, the second-order least squares estimator (SLSE) is more efficient than the ordinary least squares estimator. This result motivated the research in Gao and Zhou (J Stat Plan Inference 149:140–151, 2014), where A-optimal and D-optimal design criteria based on the SLSE were proposed and various design properties were studied. In this paper, we continue to investigate the optimal designs based on the SLSE and derive new results for the D-optimal designs. Using convex optimization techniques and moment theories, we can construct D-optimal designs for univariate polynomial and trigonometric regression models on any closed interval. Several theoretical results are obtained. The methodology is quite general. It can be applied to reduced polynomial models, reduced trigonometric models, and other regression models. It can also be extended to A-optimal designs based on the SLSE.

Suggested Citation

  • Lucy L. Gao & Julie Zhou, 2017. "D-optimal designs based on the second-order least squares estimator," Statistical Papers, Springer, vol. 58(1), pages 77-94, March.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0688-9
    DOI: 10.1007/s00362-015-0688-9
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    References listed on IDEAS

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    1. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2008. "Improving updating rules in multiplicative algorithms for computing D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 312-320, December.
    2. Holger Dette & Viatcheslav Melas & Andrey Pepelyshev, 2002. "D-Optimal Designs for Trigonometric Regression Models on a Partial Circle," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 945-959, December.
    3. Yu, Yaming, 2010. "Strict monotonicity and convergence rate of Titterington's algorithm for computing D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1419-1425, June.
    4. Liqun Wang & Alexandre Leblanc, 2008. "Second-order nonlinear least squares estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 883-900, December.
    5. Fu-Chuen Chang & Lorens Imhof & Yi-Ying Sun, 2013. "Exact $$D$$ -optimal designs for first-order trigonometric regression models on a partial circle," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 857-872, August.
    6. 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.
    7. Xiaojian Xu & Xiaoli Shang, 2014. "Optimal and robust designs for trigonometric regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 753-769, August.
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    Cited by:

    1. He, Lei, 2018. "Optimal designs for multi-factor nonlinear models based on the second-order least squares estimator," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 201-208.
    2. Mustafa Salamh & Liqun Wang, 2021. "Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors," Econometrics, MDPI, vol. 9(4), pages 1-17, November.
    3. Lei He & Rong-Xian Yue, 2022. "$$I_L$$ I L -optimal designs for regression models under the second-order least squares estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 53-66, January.
    4. Chi-Kuang Yeh & Julie Zhou, 2021. "Properties of optimal regression designs under the second-order least squares estimator," Statistical Papers, Springer, vol. 62(1), pages 75-92, February.
    5. Mustafa Salamh & Liqun Wang, 2021. "Second-Order Least Squares Method for Dynamic Panel Data Models with Application," JRFM, MDPI, vol. 14(9), pages 1-19, September.

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