Many real data analysis involve predictor variables that either cannot be measured directly or are measured with substantial error. Examples include long-term systolic blood pressure, cholesterol level, drug concentration in patient's blood, exposure to air pollutants or radioactive substances, social ability and wealth. Measurement error (ME) models are also called errors-in-variables models in econometrics, and latent variable models in psychology and other social sciences. It is well-known that statistical methods ignoring ME lead to biased and inconsistent estimates.

In statistics, the widely used estimation and inference methods are approximately consistent and therefore are applicable when the MEs are small. On the other hand, most consistent estimation methods rely on restrictive mathematical assumptions which are difficult or impossible to check in practice. Another challenging problem in nonlinear inference with ME is that the objective function to be minimized or maximized typically involves multiple integrals of no closed forms, so that the entailed numerical computation is difficult or intractable.

 In this talk, I will present a second-order least squares and a simulation-based estimation approach to general nonlinear models. I will also present a two-stage instrumental variable estimator for the censored or binary response models. All these estimators are consistent and asymptotical distributed under fairly general conditions, and they are practical and easy to implement. Monte Carlo simulations and real data examples will be used to illustrate these methods.