The Annals of Statistics

General Differential and Lagrangian Theory for Optimal Experimental Design

F. Pukelsheim and D. M. Titterington

Full-text: Open access

Abstract

The problem of optimal experimental design for estimating parameters in linear regression models is placed in a general convex analysis setting. Duality results are obtained using two approaches, one based on subgradients and the other on Lagrangian theory. The subgradient concept is also used to derive a potentially useful equivalence theorm for establishing the optimality of a singular design and, finally, general versions of the original equivalence theorems of Kiefer and Wolfowitz (1960) are obtained.

Article information

Source
Ann. Statist., Volume 11, Number 4 (1983), 1060-1068.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346321

Digital Object Identifier
doi:10.1214/aos/1176346321

Mathematical Reviews number (MathSciNet)
MR865345

Zentralblatt MATH identifier
0592.62066

JSTOR
links.jstor.org

Subjects
Primary: 62K05: Optimal designs
Secondary: 90C25: Convex programming

Keywords
Optimal design convex analysis subgradient Lagrange multipliers duality

Citation

Pukelsheim, F.; Titterington, D. M. General Differential and Lagrangian Theory for Optimal Experimental Design. Ann. Statist. 11 (1983), no. 4, 1060--1068. doi:10.1214/aos/1176346321. https://projecteuclid.org/euclid.aos/1176346321


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