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One-step ahead adaptive D-optimal design on a finite design space is asymptotically optimal

Authors
  • Pronzato, Luc1
  • 1 Université de Nice-Sophia Antipolis, Laboratoire I3S, CNRS, Bât Euclide, Les Algorithmes, 2000 route des lucioles, Sophia Antipolis Cedex, 06903, France , Sophia Antipolis Cedex (France)
Type
Published Article
Journal
Metrika
Publisher
Springer-Verlag
Publication Date
Jan 06, 2009
Volume
71
Issue
2
Pages
219–238
Identifiers
DOI: 10.1007/s00184-008-0227-y
Source
Springer Nature
Keywords
License
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Abstract

We study the consistency of parameter estimators in adaptive designs generated by a one-step ahead D-optimal algorithm. We show that when the design space is finite, under mild conditions the least-squares estimator in a nonlinear regression model is strongly consistent and the information matrix evaluated at the current estimated value of the parameters strongly converges to the D-optimal matrix for the unknown true value of the parameters. A similar property is shown to hold for maximum-likelihood estimation in Bernoulli trials (dose–response experiments). Some examples are presented.

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