Rj. Carroll et al., ASYMPTOTICS FOR THE SIMEX ESTIMATOR IN NONLINEAR MEASUREMENT ERROR MODELS, Journal of the American Statistical Association, 91(433), 1996, pp. 242-250
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.