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Asymptotic Properties of Nonlinear Least Squares Estimates in Stochastic Regression Models Over a Finite Design Space. Application to Self-Tuning Optimisation

Authors
  • Pronzato, Luc
Publication Date
Jun 06, 2009
Source
HAL
Keywords
Language
English
License
Unknown
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Abstract

We present new conditions for the strong consistency and asymptotic normality of the least squares estimator in nonlinear stochastic models when the design variables vary in a finite set. The application to self-tuning optimisation is considered, with a simple adaptive strategy that guarantees simultaneously the convergence to the optimum and the strong consistency and asymptotic normality of the estimates of the model parameters. An illustrative example is presented.

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