Optimality criteria for design in nonlinear models with constraints
type: Item
instance of: scholarly article
title: Optimality criteria for design in nonlinear models with constraints
zbMATH Open document ID: 1313.62115
author: Andrej Pázman
published in: Tatra Mountains Mathematical Publications
publication date: 2012-09-26T00:00:00Z
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 6086820
zbMATH Keywords: design of experiments
zbMATH Keywords: nonlinear regression
zbMATH Keywords: equivalence theorem
MaRDI profile type: Publication
full work available at URL: v10127-012-0014-z
OpenAlex ID: W2055646658
cites work: Q3499239
cites work: Q3716108
cites work: Optimal design of nonlinear experiments with parameter constraints
cites work: Q5511769
cites work: The Lagrangian Multiplier Test
cites work: Q4086554
DOI: 10.2478/V10127-012-0014-Z
review text: A new class of global optimality criteria for designs in nonlinear regression models with constraints is discussed. The classical global optimality criteria (such as, e.g.,~D-optimality, A-optimality or E-optimality) are based on convex function of the (asymptotic) information matrix. However, they are not directly applicable in situations with constrained parameters. The author suggests a new class of optimality criteria based on the (asymptotic) covariance matrix of the parameter estimators under the given constraints. The situation is even more complicated if, in particular, a D-optimality criterion is considered, as the covariance matrix is not of a full rank. In this situation, the author suggests to consider a simple criterion based on a function of the covariance matrix and shows that it is equivalent to consider an equivalent (reparametrized) model without restrictions on the parameters. Based on the new optimality criteria and based on the well-known equivalence theorem the author presents the necessary and sufficient conditions for an optimal design (with respect to the chosen optimality criteria).
description: scientific article; zbMATH DE number 6086820