Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments

A Monte Carlo method for estimation of the optimal design of a nonlinear parametric regression problem is presented. The basic idea is to use Monte Carlo to produce values of the error of a parametric regression estimate for randomly chosen designs and randomly chosen parameters; then, using this data, nonparametric regression is used to estimate the design for which the maximal expected error with respect to all possible parameter values is minimal. A theoretical result concerning the consistency of the optimal design estimate is presented, and the method is used to find an optimal design for an experimental fatigue test.