The effects of measurement error on parameter estimation

Abstract

This paper presents a general formulation of the errors-in-variables problem, which encompasses both linear and nonlinear models, functional and structural cases, and dependent measurement errors. It is assumed that the parameter of interest is estimated by an M -estimator which is consistent in the absence of measurement error, and it is shown how to assess the asymptotic bias in this estimator when error is present, and how to construct an estimator with smaller bias. The method requires knowledge or estimability of the measurement error variance. The application of this technique to the class of generalized linear models is studied in some detail; asymptotic distributions are derived and results from a small Monte Carlo study are presented.