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Robust designs for misspecified exponential regression models

✍ Scribed by Xiaojian Xu

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
161 KB
Volume
25
Category
Article
ISSN
1524-1904

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✦ Synopsis

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 Β© 2009 John Wiley & Sons, Ltd.

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