Estimation in a simple linear regression model with measurement error

TL;DR

This paper addresses bias in estimating the slope in simple linear regression with measurement errors, proposing bias reduction methods and truncation procedures to improve estimator accuracy.

Contribution

It introduces a general bias reduction procedure and exact estimators for finite samples in models with measurement errors in independent variables.

Findings

Bias-reduced estimators outperform ordinary least squares in finite samples.

Truncation procedures improve mean square errors of estimators.

Proposed methods effectively reduce bias caused by measurement errors.

Abstract

This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause biasedness of the ordinary least squares estimator. A general procedure for the bias reduction is presented in a finite sample situation, and some exact bias-reduced estimators are proposed. Also, it is shown that certain truncation procedures improve the mean square errors of the ordinary least squares and the bias-reduced estimators.