, Volume 71, Issue 2, pp 219–238 | Cite as

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

  • Luc Pronzato


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.


Adaptive design Consistency D-Optimal design Sequential design 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Laboratoire I3S, CNRSUniversité de Nice-Sophia AntipolisSophia Antipolis CedexFrance

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