The Annals of Statistics

On G-efficiency calculation for polynomial models

Holger Dette and Weng Kee Wong

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Abstract

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

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

Dates
First available in Project Euclid: 15 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1034713648

Digital Object Identifier
doi:10.1214/aos/1034713648

Mathematical Reviews number (MathSciNet)
MR1389866

Zentralblatt MATH identifier
0854.62066

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1034713648


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