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Lack-of-fit-efficiently optimal designs to estimate the highest coefficient of a polynomial with large degree

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  • Bischoff, Wolfgang
  • Miller, Frank

Abstract

To check regression models Bischoff and Miller (2006a. Optimal designs which are efficient for lack of fit tests. Ann. Stat., to appear.) introduced optimal designs to estimate a parameter in the class of designs which guarantee a certain efficiency with respect to the power of a lack of fit (LOF-) test. One part of such an optimal design is absolutely continuous with respect to the Lebesgue measure and the other part consists of a finite number of mass points. The optimal design to estimate the highest coefficient of a polynomial regression of fixed degree k-1 (ek-optimal design) in the class of designs with LOF-efficiency of at least r has the same mass points as the classical ek-optimal design if r is small enough. In this paper we investigate the set of efficiencies r with that property.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:15:p:1701-1704
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    2. 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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