Abstract: This work proposes a sequential procedure to select the best model among several nested non-linear models and to estimate efficiently the parameters of the chosen model. At the first step of this procedure, a generalized DKL-optimum design is computed that is optimal for the goals of model selection and parameter estimation. Subsequently, at each step, an adaptive generalized DKL-optimum design is computed from the data accrued and the tests previously performed. The proposed sequential scheme selects the best non-linear model with probability converging to one; moreover it allows efficient estimates of parameters, since the adaptive sequential DKL-optimum designs converge to the D-optimum design for the ``true'' model.
Key words and phrases: Argmin processes, convexity, D-optimality, KL-optimality, DKL-optimality, log-likelihood ratio test, semi-continuity, sequential design of experiments, stochastic convergence.