Corrected score function for errors-in-variables models: Methodology and application to generalized linear models

Statistical models whose independent variables are subject to measurement errors are often referred to as ‘errors-in-variables models’. To correct for the effects of measurement error on parameter estimation, this paper considers a correction for score functions. A corrected score function is one whose expectation with respect to the measurement error distribution coincides with the usual score function based on the unknown true independent variables. This approach makes it possible to do inference as well as estimation of model parameters without additional assumptions. The corrected score functions of some generalized linear models are obtained.