Open Access
June, 1982 Optimal Robust Designs: Linear Regression in $R^k$
L. Pesotchinsky
Ann. Statist. 10(2): 511-525 (June, 1982). DOI: 10.1214/aos/1176345792


The model $E(y \mid x) = \theta_0 + \sum^k_{i=1} \theta_ix_i + \psi(\mathbf{x})$ is considered, where $\psi(\mathbf{x})$ is an unknown contamination with $| \psi(\mathbf{x})|$ bounded by given $\varphi(\mathbf{x})$. Optimal designs are studied in terms of least squares estimation and a family of minimax criteria. In particular, analogs of D-, A- and E-optimal designs are studied in the general case of an arbitrary $k$. Some commonly used integer designs are considered and their efficiencies with respect to optimal designs are determined. In particular, it is shown that star-point designs or regular replicas of $2^k$ factorials are very efficient under the appropriate choice of levels of factors.


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L. Pesotchinsky. "Optimal Robust Designs: Linear Regression in $R^k$." Ann. Statist. 10 (2) 511 - 525, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0489.62065
MathSciNet: MR653526
Digital Object Identifier: 10.1214/aos/1176345792

Primary: 62K05
Secondary: 62G35 , 62J05

Keywords: $D$-optimality , $E$-optimality , Linear regression , optimal design , robust design

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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