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.
Publié le : 1982-06-14
Classification:
$D$-optimality,
$E$-optimality,
linear regression,
optimal design,
robust design,
62K05,
62G35,
62J05
@article{1176345792,
author = {Pesotchinsky, L.},
title = {Optimal Robust Designs: Linear Regression in $R^k$},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 511-525},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345792}
}
Pesotchinsky, L. Optimal Robust Designs: Linear Regression in $R^k$. Ann. Statist., Tome 10 (1982) no. 1, pp. 511-525. http://gdmltest.u-ga.fr/item/1176345792/