Admissible experimental designs in multiple polynomial regression
type: Item
instance of: scholarly article
title: Admissible experimental designs in multiple polynomial regression
zbMATH Open document ID: 0756.62029
DOI: 10.1016/0378-3758(92)90031-M
published in: Journal of Statistical Planning and Inference
publication date: 1992-09-27T00:00:00Z
review text: This paper provides connection between admissibility of a design in a multiple regression set up on \(\nu\) variables and admissibility of subdesigns in less than \(\nu\) variables. The admissibility is with respect to any design optimality criterion. It is shown that for a convex experimental region, an admissible linear regression design is concentrated on its extreme points, and an admissible quadratic regression design has at most one support point in the relative interior of an arbitrary face of the region.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62K99
zbMATH DE Number: 63590
zbMATH Keywords: Löwner partial ordering
zbMATH Keywords: approximate design
zbMATH Keywords: invariant design
zbMATH Keywords: multiple polynomial regression
zbMATH Keywords: information matrix
zbMATH Keywords: admissibility of subdesigns
zbMATH Keywords: convex experimental region
zbMATH Keywords: admissible linear regression design
zbMATH Keywords: extreme points
zbMATH Keywords: admissible quadratic regression design
author: Berthold Heiligers
reviewed by: D. Raghavarao
MaRDI profile type: Publication
cites work: Optimal and Efficient Designs of Experiments
cites work: Q3240572
cites work: Q5588210
cites work: Further characterizations of design optimality and admissibility for partial parameter estimation in linear regression
cites work: Comparison of rotatable designs for regression on balls. I. (quadratic)
cites work: Comparison of design for quadratic regression of cubes
cites work: Q3960954
cites work: Q3995383
cites work: Admissibility of experimental designs in linear regression with constant term
cites work: Invariant admissible and optimal designs in cubic regression on the \(\nu\)-ball
cites work: Optimal Experimental Designs
cites work: Q3844024
cites work: Optimum Designs in Regression Problems, II
cites work: General equivalence theory for optimum designs (approximate theory)
cites work: Q4072671
cites work: The Equivalence of Two Extremum Problems
cites work: Q5538609
cites work: Efficient \(D_ s\)-optimal designs for multivariate polynomial regression on the q-cube
cites work: Inequalities: theory of majorization and its applications
cites work: D-optimum and quasi-D-optimum second-order designs on a cube
cites work: \(\Phi_p\)-optimal second order designs for symmetric regions
cites work: Information Increasing Orderings in Experimental Design Theory
cites work: Q5638112
full work available at URL: 0378-3758(92)90031-m
OpenAlex ID: W2006773033
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description: scientific article; zbMATH DE number 63590