One-step ahead adaptive D-optimal design on a finite design space is asymptotically optimal |
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Authors: | Luc Pronzato |
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Institution: | 1. Laboratoire I3S, CNRS, Université de Nice-Sophia Antipolis, Bat Euclide, Les Algorithmes, 2000 route des lucioles, BP 121, 06903, Sophia Antipolis Cedex, France
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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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