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Excess of locally D-optimal designs for Cobb–Douglas model

Author

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  • Yu. D. Grigoriev

    (St. Petersburg State Electrotechnical University)

  • V. B. Melas

    (St. Petersburg State University)

  • P. V. Shpilev

    (St. Petersburg State University)

Abstract

In this paper we study the problem of homothety’s influence on the number of optimal design support points under fixed values of a regression model’s parameters. The Cobb–Douglas two-dimensional nonlinear in parameters model used in microeconomics is considered. There exist two types of optimal designs: saturated (i.e. design with the number support points equal to the number of parameters) and excess design (i.e. design with greater number of support points). The optimal designs with the minimal number of support points are constructed explicitly. Numerical methods for constructing designs with greater number of points are used.

Suggested Citation

  • Yu. D. Grigoriev & V. B. Melas & P. V. Shpilev, 2018. "Excess of locally D-optimal designs for Cobb–Douglas model," Statistical Papers, Springer, vol. 59(4), pages 1425-1439, December.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1022-0
    DOI: 10.1007/s00362-018-1022-0
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    References listed on IDEAS

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    1. Jesus Felipe & F. Gerard Adams, 2005. ""A Theory of Production" The Estimation of the Cobb-Douglas Function: A Retrospective View," Eastern Economic Journal, Eastern Economic Association, vol. 31(3), pages 427-445, Summer.
    2. Douglas, Paul H, 1976. "The Cobb-Douglas Production Function Once Again: Its History, Its Testing, and Some New Empirical Values," Journal of Political Economy, University of Chicago Press, vol. 84(5), pages 903-915, October.
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    Cited by:

    1. Yu. D. Grigoriev & V. B. Melas & P. V. Shpilev, 2021. "Excess and saturated D-optimal designs for the rational model," Statistical Papers, Springer, vol. 62(3), pages 1387-1405, June.

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