Experiment design in a bounded-error context: Comparison with D-optimality

doi:10.1016/0005-1098(89)90006-X

Automatica

Volume 25, Issue 3, May 1989, Pages 383-391

https://doi.org/10.1016/0005-1098(89)90006-X Get rights and content

Abstract

The problem of optimal experiment design for linear regression models is addressed. The measurement errors are supposed to be bounded, with no other hypothesis on their distribution, contrary to the classical statistical approach. An experiment is considered here as optimal if it minimizes the volume of the set of all parameters that are consistent with the data, the model structure, and the noise bounds. This new design policy is compared to the classical D-optimal design used in a statistical context. When the number of measurements is equal to the number of parameters to be estimated, the new optimality criterion, although relying on quite different hypotheses on the noise distribution, is shown to lead to the same optimal policy as a D-optimality criterion. This is no longer true when more measurements are to be made. Depending on the shape of the admissible experimental domain, it is sometimes possible to design optimal experiments without any calculations. An algorithmic procedure is suggested, to be used when this is not so.

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Experiment design for bounded-error models
1990, Mathematics and Computers in Simulation
The problem of experiment design for parameter bounding is addressed. The measurement errors are assumed to be bounded, with no other hypothesis on their distribution. An experiment is defined as optimal when it minimizes the volume of the set of the parameters that are consistent with the data, model structure, and error bounds. Linear and nonlinear model structures are considered, with special attention to situations where the set of consistent parameters may be disconnected.

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^☆: The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Y. Sunahara under the direction of Editor P. C. Parks.

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PaperExperiment design in a bounded-error context: Comparison with D-optimality☆

Abstract

Math. Comput. Simul.

Automatica

Chem. Engng Sci.

Automatica

Math. Comput. Simul.

Math. Biosci.

Math. Biosci.

Math. Comput. Simul.

The design of experiments for parameter estimation

Technometrics

Optimal sampling schedule with unknown but bounded measurement errors: families of linear models

Optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors

IEEE Trans. Aut. Control

Recursive state estimation for a set-membership description of uncertainty

IEEE Trans. Aut. Control

Design of experiments in nonlinear situations

Biometrika

The experimental study of physical mechanisms

Technometrics

The occurrence of replications in optimal design of experiments to estimate parameters in nonlinear models

J. R. Statist. Soc.

Some experiences with a nonlinear experimental design criterion

Technometrics

Discussion on a paper by H. P. Wynn

J. R. Statist. Soc.

Optimal Bayesian design for nonlinear estimation

Locally optimal designs for estimating parameters

Ann. Math. Statist.

Paper
Experiment design in a bounded-error context: Comparison with D-optimality☆