Linear and nonlinear regression with covariate measurement error

Many real data analyses 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 engineering, and latent variable models in psychology and other social sciences.  It is well-known that statistical models ignoring ME lead to biased and inconsistent estimates.

In statistics, the widely used methods for estimation and inference 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 computationis difficult or intractable.

In this talk, the adverse impacts of ME will be demonstrated in a simple linear regression set-up.  Moments-based approaches to estimation in general linear and nonlinear models will then be proposed.  A two-stage instrumental variable estimator for models with censored or binary response variables will also be presented.  All these estimators are consistent and asymptotically normally distributed under fairly general conditions, and they are practical and numerically feasible.  Monte Carlo simulations and real data examples will be used to illustrate these methods.

This talk will be on video conference in Sunlife 1404 (Edmonton).