## The Annals of Statistics

- Ann. Statist.
- Volume 16, Number 3 (1988), 1225-1240.

### Efficient $D_s$-Optimal Designs for Multivariate Polynomial Regression on the $q$-Cube

#### Abstract

Polynomial regression in $q$ variables of degree $n$ on the $q$-cube is considered. Approximate $D$-optimal and approximate $D_s$-optimal designs for estimating higher degree terms are investigated. Numerical results are given for $n = 2$ with arbitrary $q$ and for $n = 3, 4, 5$ and $q = 2, 3$. Exact solutions are given within the class of product designs together with some efficiency calculations.

#### Article information

**Source**

Ann. Statist., Volume 16, Number 3 (1988), 1225-1240.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176350957

**Digital Object Identifier**

doi:10.1214/aos/1176350957

**Mathematical Reviews number (MathSciNet)**

MR959198

**Zentralblatt MATH identifier**

0664.62075

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62K05: Optimal designs

Secondary: 62J05: Linear regression

**Keywords**

$D_s$-optimal designs symmetric designs product designs polynomial regression on the $q$-cube canonical moments

#### Citation

Lim, Yong B.; Studden, W. J. Efficient $D_s$-Optimal Designs for Multivariate Polynomial Regression on the $q$-Cube. Ann. Statist. 16 (1988), no. 3, 1225--1240. doi:10.1214/aos/1176350957. https://projecteuclid.org/euclid.aos/1176350957