Model selection and parameter estimation in non-linear nested models: a sequential generalized DKL-optimum design

This work proposes a sequential procedure which is useful 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, which is optimal for the double goal of model selection and parameter estimation. Subsequently, at each following step, an adaptive generalized DKL-optimum design is computed on the base of the data accrued and tests previously performed. The proposed sequential scheme selects the best non-linear model with probability converging to one; moreover it estimates efficiently its parameters, since the adaptive sequential DKL-optimum designs converge to the D-optimum design for the “true” model. AMS 2000 subject classifications: Primary 62K05, 60B10; secondary 62L05, 60B05.