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D-optimal designs for polynomial regression with exponential weight function

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Abstract

Weighted polynomial regression with exponential weight function on an interval is considered. The D-optimal designs are completely characterized via three differential equations. Some invariant properties of the optimal designs under affine transformation are derived. The optimal design as degree of polynomial goes to infinity, is shown to converge weakly to the arcsin distribution. Comparisons of the optimal designs with the arcsin distribution are also made.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan, ROC

    Fu-Chuen Chang, Hsiu-Ching Chang & Sheng-Shian Wang

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  1. Fu-Chuen Chang
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  2. Hsiu-Ching Chang
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  3. Sheng-Shian Wang
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Correspondence to Fu-Chuen Chang.

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Chang, FC., Chang, HC. & Wang, SS. D-optimal designs for polynomial regression with exponential weight function. Metrika 70, 339–354 (2009). https://doi.org/10.1007/s00184-008-0195-2

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  • DOI: https://doi.org/10.1007/s00184-008-0195-2

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