Asymptotic properties of simple linear measurement error models

E Dagalp,Rukiye Rukiye

doi: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.

Highlights

The regression analysis is a statistical methodology for studying the functional relationship between two or more quantitative variables so that one can be explained from the other variables
C 2011 Ankara University measured with a substitute variable causes a common problem that is called attenuation, in other words measurement error problem
When measurement error is in presence, the statistical models and methods for analyzing the such data is studied by Fuller and Hidiroglou (1978), Moran (1971) and recently Prentice (1982), Wolter and Fuller (1982a, 1982b), Carroll et al(1984), Stefanski (1985) and Stefanski and Carroll (1985)

Summary

ASYMPTOTIC PROPERTIES OF SIMPLE LINEAR MEASUREMENT ERROR MODELS

. The main objective 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. 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. The effect of measurement error on fitting a regression model causes inconsistent parameter estimation and its statistical inferences.

Consider the simple linear regression model of Y on X

Consider the joint density in and define

Suppose that there exists a certain smooth Ψ functions such that

Carlo runs