Admissible and optimal exact designs for polynomial regression
type: Item
instance of: scholarly article
title: Admissible and optimal exact designs for polynomial regression
zbMATH Open document ID: 0616.62102
DOI: 10.1016/0378-3758(87)90052-8
author: Kenneth B. Constantine
author: Yong B. Lim
author: William J. Studden
published in: Journal of Statistical Planning and Inference
publication date: 1987-01-01T00:00:00Z
review text: The authors' interest is to address some classical optimal design questions in the context of the exact design setting for the polynomial regression model. Let \(x_ 0,...,x_ l\) denote the distinct levels at which \(n_ 0,...,n_ l\) observations are to be taken. Here \(n_ 0+...+n_ l=N\). An exact design \(\xi^ N\) is a probability measure on [a,b] which concentrates mass \(n_ i/N\) at each \(x_ i\). Let \(M(\xi^ N)\) denote the information matrix (per observation) of an exact design \(\xi^ N\). An exact design \(\xi^ N\) is said to be admissible if and only if there exists no other exact design \({\tilde \xi}^ N\) such that \(M(\xi^ N)\neq M({\tilde \xi}^ N)\) and \(M(\xi^ N)\leq M({\tilde \xi}^ N)\). Solution of this problem will enable us to restrict our search for an optimal design to the class of admissible designs. A necessary condition for an exact design to be admissible is provided. It is conjectured that this condition is also sufficient and the basis for the conjecture is discussed. It is shown that the Salaevskij's conjecture holds for cubic regression. The interesting forms of G-optimal exact designs are indicated.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 3999049
zbMATH Keywords: exact design
zbMATH Keywords: polynomial regression
zbMATH Keywords: admissible designs
zbMATH Keywords: Salaevskij's conjecture
zbMATH Keywords: G-optimal exact designs
MaRDI profile type: Publication
full work available at URL: 0378-3758(87)90052-8
OpenAlex ID: W2004295201
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description: scientific article; zbMATH DE number 3999049