Jr. Cook et La. Stefanski, SIMULATION-EXTRAPOLATION ESTIMATION IN PARAMETRIC MEASUREMENT ERROR MODELS, Journal of the American Statistical Association, 89(428), 1994, pp. 1314-1328
We describe a simulation-based method of inference for parametric meas
urement error models in which the measurement error variance is known
or at least well estimated. The method entails adding additional measu
rement error in known increments to the data, computing estimates from
the contaminated data, establishing a trend between these estimates a
nd the variance of the added errors, and extrapolating this trend back
to the case of no measurement error. We show that the method is equiv
alent or asymptotically equivalent to method-of-moments estimation in
linear measurement error modeling. Simulation studies are presented sh
owing that the method produces estimators that are nearly asymptotical
ly unbiased and efficient in standard and nonstandard logistic regress
ion models. An oversimplified but fairly accurate description of the m
ethod is that it is method-of-moments estimation using Monte Carlo-der
ived estimating equations.