ASYMPTOTICS FOR THE SIMEX ESTIMATOR IN NONLINEAR MEASUREMENT ERROR MODELS

Cook and Stefanski have described a computer-intensive method, the SIM EX method, for approximately consistent estimation in regression probl ems with additive measurement error. In this article we derive the asy mptotic distribution of their estimators and show how to compute estim ated standard errors. These standard error estimators can either be us ed alone or as prepivoting devices in a bootstrap analysis. We also gi ve theoretical justification to some of the phenomena observed by Cook and Stefanski in their simulations.