Admissibility of experimental designs in linear regression with constant term
type: Item
instance of: scholarly article
title: Admissibility of experimental designs in linear regression with constant term
zbMATH Open document ID: 0734.62079
DOI: 10.1016/0378-3758(91)90064-L
author: Berthold Heiligers
published in: Journal of Statistical Planning and Inference
publication date: 1991-01-01T00:00:00Z
review text: The paper provides the mathematical and statistical details for formulating the optimality problem of designs in the linear regression setting with a constant term. In the usual notation and jargon the determination of an optimal design calls for the solution of a minimization problem, which is not an easy task. The subsets of admissible designs and invariant designs are brought into play in order to reduce the minimization effort. Specifically, the author establishes necessary conditions for admissibility whenever the regression function contains a constant term. It is further shown that the information matrix of an admissible design maximizes a linear function under certain linear restrictions. This in turn solves an unconstrained nonconstant linear optimization problem, which yields nontrivial conditions on the support points similar to the classical results of \textit{S. Karlin} and \textit{W. J. Studden} [see Ann. Math. Statistics 37, 783-815 (1966; Zbl 0151.239)]. The polynomial regression is selected as an example. For the linear setup all invariant and admissible designs are presented. In the quadratic case the support points of an invariant and admissible design are either zero or special boundary points of the experimental region.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62C15
zbMATH DE Number: 4215213
zbMATH Keywords: Loewner partial ordering
zbMATH Keywords: approximate design
zbMATH Keywords: moment matrix
zbMATH Keywords: generalized Chebyshev inequality
zbMATH Keywords: multiple polynomial regression
zbMATH Keywords: minimization problem
zbMATH Keywords: admissible designs
zbMATH Keywords: invariant designs
zbMATH Keywords: information matrix
zbMATH Keywords: linear restrictions
reviewed by: B. Leo Raktoe
MaRDI profile type: Publication
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full work available at URL: 0378-3758(91)90064-l
OpenAlex ID: W1988234729
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description: scientific article; zbMATH DE number 4215213