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

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 of the estimates of the model parameters. An illustrative example is presented.