The Annals of Statistics

On G-efficiency calculation for polynomial models

Holger Dette and Weng Kee Wong

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We study properties of the variance function of the least squares estimator for the response surface. For polynomial models, we identify a class of approximate designs for which their variance functions are maximized at the extreme points of the design space. As an application, we examine robustness properties of D-optimal designs and $D_{n-r}$-optimal designs under various polynomial model assumptions. Analytic formulas for the G-efficiencies of these designs are derived, along with their D-efficiencies.

Article information

Ann. Statist., Volume 23, Number 6 (1995), 2081-2101.

First available in Project Euclid: 15 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 65D30: Numerical integration

Approximate designs canonical moments $D$- and $G$-optimal designs $D_{n-r}$-optimal designs homoscedasticity information matrix orthogonal polynomials


Dette, Holger; Wong, Weng Kee. On G -efficiency calculation for polynomial models. Ann. Statist. 23 (1995), no. 6, 2081--2101. doi:10.1214/aos/1034713648.

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