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

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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Luc Pronzato. One-step ahead adaptive D-optimal design on a finite design space is asymptotically optimal. Metrika, Springer Verlag, 2010, 71 (2), pp.219-238. ⟨10.1007/s00184-008-0227-y⟩. ⟨hal-00396975⟩

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