CORRECTED SCORE FUNCTIONS IN CLASSICAL ERROR‐IN‐VARIABLES AND INCIDENTAL PARAMETER MODELS

Abstract

Summary Nakamura (1990) introduced an approach to estimation in measurement error models based on a corrected score function, and claimed that the estimators obtained are consistent for functional models. Proof of the claim essentially assumed the existence of a corrected log‐likelihood for which differentiation with respect to model parameters can be interchanged with conditional expectation taken with respect to the measurement error distributions, given the response variables and true covariates. This paper deals with simple yet practical models for which the above assumption is false, i.e. a corrected score function for the model may not be obtained through differentiating a corrected log‐likelihood although it exists. Alternative regularity conditions with no reference to log‐likelihood are given, under which the corrected score functions yield consistent and asymptotically normal estimators. Application to functional comparative calibration yields interesting results.