IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v58y2017i1d10.1007_s00362-015-0688-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0688-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-015-0688-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Granjo, Jose F.O & Oliveira, Nuno M.C, 2022. "Optimal design of experiments for implicit models," LSE Research Online Documents on Economics 107584, London School of Economics and Political Science, LSE Library.
    2. Belmiro P. M. Duarte, 2023. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    3. Radoslav Harman & Eva Benková, 2017. "Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 201-225, February.
    4. Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.
    5. Xiaojian Xu & Xiaoli Shang, 2017. "D-optimal designs for full and reduced Fourier regression models," Statistical Papers, Springer, vol. 58(3), pages 811-829, September.
    6. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Granjo, Jose F.O & Oliveira, Nuno M.C, 2019. "Optimal design of experiments for liquid–liquid equilibria characterization via semidefinite programming," LSE Research Online Documents on Economics 102500, London School of Economics and Political Science, LSE Library.
    7. Pronzato, Luc, 2013. "A delimitation of the support of optimal designs for Kiefer’s ϕp-class of criteria," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2721-2728.
    8. Monica Dessole & Fabio Marcuzzi & Marco Vianello, 2020. "dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
    9. Duarte, Belmiro P.M. & Sagnol, Guillaume & Wong, Weng Kee, 2018. "An algorithm based on semidefinite programming for finding minimax optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 99-117.
    10. Harman, Radoslav & Jurík, Tomás, 2008. "Computing c-optimal experimental designs using the simplex method of linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 247-254, December.
    11. Dedi Rosadi & Shelton Peiris, 2014. "Second-order least-squares estimation for regression models with autocorrelated errors," Computational Statistics, Springer, vol. 29(5), pages 931-943, October.
    12. 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.
    13. 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.
    14. Alqallaf, Fatemah & Huda, S., 2013. "Minimax designs for the difference between two estimated responses in a trigonometric regression model," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 909-915.
    15. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2014. "‘Nearly’ universally optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1103-1112.
    16. D. Rosadi & P. Filzmoser, 2019. "Robust second-order least-squares estimation for regression models with autoregressive errors," Statistical Papers, Springer, vol. 60(1), pages 105-122, February.
    17. Maria Karlsson & Thomas Laitila, 2014. "Finite mixture modeling of censored regression models," Statistical Papers, Springer, vol. 55(3), pages 627-642, August.
    18. 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.
    19. 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.
    20. Fei Jiang & Yanyuan Ma & J. Jack Lee, 2017. "A second-order semiparametric method for survival analysis, with application to an acquired immune deficiency syndrome clinical trial study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 833-846, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0688-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.