ASYMPTOTIC PROPERTIES OF SIMPLE LINEAR MEASUREMENT ERROR MODELS

Year 2011, Volume: 60 Issue: 1, 71 - 84, 01.02.2011

Rukiye E. Dagalp

https://doi.org/10.1501/Commua1_0000000670

Abstract

The main ob jective of this paper is to study estimators of regression models on the independent variable X which is not directly observed
for some reasons. In such a situation, a substitute variable W is observed
instead. This substitution complicates the statistical analysis of the observed
data when the purpose of the analysis is inference about a model defined in
terms of X. The substitution causes a inconsistent estimator; this is defined as
a measurement error problem. To correct this problem, the conditional score
and corrected score methods are proposed by Stefanski&Carroll (1985) and
Nakamura (1990), respectively. In this study, large sample distribution theory for both the conditional score and corrected score estimators are derived
and the performance of the estimators and the adequacy of the large sample
distribution theory are obtained via Monte Carlo simulation.

Keywords

Conditional score function, Corrected score function, functionalmodel, generalized linear models, measurement error models, error-free and error-prone predictors, error in variables, M-estimator