## The Annals of Statistics

- Ann. Statist.
- Volume 10, Number 2 (1982), 511-525.

### Optimal Robust Designs: Linear Regression in $R^k$

#### Abstract

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.

#### Article information

**Source**

Ann. Statist., Volume 10, Number 2 (1982), 511-525.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345792

**Digital Object Identifier**

doi:10.1214/aos/1176345792

**Mathematical Reviews number (MathSciNet)**

MR653526

**Zentralblatt MATH identifier**

0489.62065

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62K05: Optimal designs

Secondary: 62G35: Robustness 62J05: Linear regression

**Keywords**

$D$-optimality $E$-optimality linear regression optimal design robust design

#### Citation

Pesotchinsky, L. Optimal Robust Designs: Linear Regression in $R^k$. Ann. Statist. 10 (1982), no. 2, 511--525. doi:10.1214/aos/1176345792. https://projecteuclid.org/euclid.aos/1176345792