General differential and Lagrangian theory for optimal experimental design
type: Item
instance of: scholarly article
title: General differential and Lagrangian theory for optimal experimental design
zbMATH Open document ID: 0592.62066
published in: The Annals of Statistics
publication date: 1983-01-01T00:00:00Z
review text: The paper provides a treatment of optimal experimental designs using the differential theory of convex analysis with the concept of the subgradient. Also included is a Lagrangian duality treatment. This paper is closely related to the first author's paper in J. Stat. Plann. Inference 4, 339-364 (1980; Zbl 0472.62079). The interest lies in estimating s linearly independent linear functions of the unknown parameters. The main result is the proof of a theorem on duality in terms of subgradients. This result is also proved applying to strong Lagrangian principle. For singular information matrices an optimality condition formulated by \textit{S. D. Silvey} [Biometrika 65, 553-559 (1978; Zbl 0391.62054)] is proved to be necessary. The equivalence result of \textit{J. Kiefer} and \textit{J. Wolfowitz} [Can. J. Math. 12, 363-366 (1960; Zbl 0093.156)] is extended to information functionals.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 90C52
zbMATH DE Number: 3951832
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: differential theory of convex analysis
zbMATH Keywords: subgradient
zbMATH Keywords: duality
zbMATH Keywords: Lagrangian principle
zbMATH Keywords: singular information matrices
zbMATH Keywords: optimality
zbMATH Keywords: information functionals
author: Friedrich Pukelsheim
author: D. M. Titterington
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346321
OpenAlex ID: W1521454485
DOI: 10.1214/AOS/1176346321
description: scientific article; zbMATH DE number 3951832