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.