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Robust designs for misspecified exponential regression models

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  • Xiaojian Xu

Abstract

We consider the construction of designs for exponential regression. The response function is an only approximately known function of a specified exponential function. As well, we allow for variance heterogeneity. We find minimax designs and corresponding optimal regression weights in the context of the following problems: (1) for nonlinear least‐squares (LS) estimation with homoscedasticity, determine a design to minimize the maximum value of the integrated mean‐squared error (IMSE), with the maximum being evaluated for the possible departures from the response function; (2) for nonlinear LS estimation with heteroscedasticity, determine a design to minimize the maximum value of IMSE, with the maximum being evaluated over both types of departures; (3) for nonlinear weighted LS estimation, determine both weights and a design to minimize the maximum IMSE; and (4) choose weights and design points to minimize the maximum IMSE, subject to a side condition of unbiasedness. Solutions to (1)–(4) are given in complete generality. Copyright © 2009 John Wiley & Sons, Ltd.

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  • Xiaojian Xu, 2009. "Robust designs for misspecified exponential regression models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 179-193, March.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:2:p:179-193
    DOI: 10.1002/asmb.739
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    Cited by:

    1. Konstantinou, Maria & Biedermann, Stefanie & Kimber, Alan, 2017. "Model robust designs for survival trials," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 239-250.

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