Efficient \(D_ s\)-optimal designs for multivariate polynomial regression on the q-cube
type: Item
instance of: scholarly article
title: Efficient \(D_ s\)-optimal designs for multivariate polynomial regression on the q-cube
zbMATH Open document ID: 0664.62075
author: Yong B. Lim
author: William J. Studden
published in: The Annals of Statistics
publication date: 1988-01-01T00:00:00Z
review text: This is a paper within the classical world of KIEFER's optimal experimental design. Approximate \(D_ s\)-optimal designs for polynomial regression in q variables of degree n on the q-dimensional unit-cube are considered. Especially, for \(n=2\) a complete description of the \(D_ s\)- optimal designs for estimating only the quadratic terms is given. For \(n=3,4,5\) and \(q=2,3\) numerical results are presented which support the general idea that D- and \(D_ s\)-optimal designs are ``close to'' product designs. Therefore, in the last section, \(D_ s\)-optimal product designs are described by use of canonical moments and, indeed, they show high efficiencies.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 4086805
zbMATH Keywords: approximate D-optimal designs
zbMATH Keywords: estimating higher degree terms
zbMATH Keywords: efficiency calculations
zbMATH Keywords: symmetric designs
zbMATH Keywords: q-cube
zbMATH Keywords: Ds-optimality
zbMATH Keywords: polynomial regression
zbMATH Keywords: numerical results
zbMATH Keywords: product designs
zbMATH Keywords: canonical moments
reviewed by: Wolfgang Näther
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350957
OpenAlex ID: W1992271704
DOI: 10.1214/AOS/1176350957
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description: scientific article; zbMATH DE number 4086805