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Designs for approximately linear regression: two optimality properties of uniform designs

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  • Wiens, Douglas P.

Abstract

We study regression designs, with an eye to maximizing the minimum power of the standard test for Lack of Fit. The minimum is taken over a broad class of departures from the assumed multiple linear regression model. We show that the uniform design is maximin. This design attains its optimality by maximizing the minimum bias in the regression estimate of [sigma]2. It is thus surprising that this same design has an optimality property relative to the estimation of [sigma]2 -- it minimizes the maximum bias, in a closely related class of departures from linearity.

Suggested Citation

  • Wiens, Douglas P., 1991. "Designs for approximately linear regression: two optimality properties of uniform designs," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 217-221, September.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:3:p:217-221
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    Citations

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    Cited by:

    1. Bischoff, Wolfgang & Miller, Frank, 2006. "Lack-of-fit-efficiently optimal designs to estimate the highest coefficient of a polynomial with large degree," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1701-1704, September.
    2. Hengzhen Huang & Hong†Bin Fang & Ming T. Tan, 2018. "Experimental design for multi†drug combination studies using signaling networks," Biometrics, The International Biometric Society, vol. 74(2), pages 538-547, June.
    3. Ramón Ardanuy & J. López-Fidalgo & Patrick Laycock & Weng Wong, 1999. "When is an Equally-Weighted Design D-optimal?," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 531-540, September.
    4. Dette, Holger & Wiens, Douglas P., 2007. "Robust designs for 3D shape analysis with spherical harmonic descriptors," Technical Reports 2007,12, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Huang, Hengzhen & Chen, Xueping, 2021. "Compromise design for combination experiment of two drugs," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    6. 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.
    7. Wiens, Douglas P., 2010. "Robustness of design for the testing of lack of fit and for estimation in binary response models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3371-3378, December.
    8. Douglas P. Wiens, 2009. "Robust discrimination designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 805-829, September.
    9. Renata Eirini Tsirpitzi & Frank Miller & Carl-Fredrik Burman, 2023. "Robust optimal designs using a model misspecification term," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 781-804, October.
    10. 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.
    11. Biedermann, Stefanie & Dette, Holger, 2000. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Technical Reports 2000,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    12. Biedermann, Stefanie & Dette, Holger, 2001. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 215-224, April.
    13. Mandal, Nripes Kumar & Pal, Manisha, 2013. "Maximin designs for the detection of synergistic effects," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1632-1637.

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