Totally positive regression: E-optimal designs
type: Item
instance of: scholarly article
title: Totally positive regression: E-optimal designs
zbMATH Open document ID: 1020.62064
author: Berthold Heiligers
published in: Metrika
publication date: 2003-03-25T00:00:00Z
review text: E-optimality of approximate designs in linear regression models is paired with a dual problem of nonlinear Chebyshev approximation. When the regression functions form a totally positive system, then the information matrices of designs for subparameters turn out to be ``almost'' totally positive, a property which allows to solve the nonlinear Chebyshev problem. Thereby we obtain explicit formulae for E -optimal designs in terms of equi-oscillating generalized polynomials. The considerations unify and generalize known results on E-optimality for particular regression setups.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 1887584
zbMATH Keywords: approximate design
zbMATH Keywords: scalar optimality
zbMATH Keywords: Chebyshev approximation
zbMATH Keywords: Chebyshev system
zbMATH Keywords: E-optimality
zbMATH Keywords: equi-oscillation
zbMATH Keywords: polynomial splines
zbMATH Keywords: total positivity
zbMATH Keywords: weighted polynomial regression
MaRDI profile type: Publication
full work available at URL: s184-002-8364-7
OpenAlex ID: W2083758994
DOI: 10.1007/S184-002-8364-7
description: scientific article; zbMATH DE number 1887584