Weighted Stochastic Restricted Estimation in Linear Measurement Error Models

Abstract

Abstract This article discusses the consistent estimation of the parameters in a linear measurement error model when stochastic linear restrictions on regression coefficients are available. We propose some methodologies to obtain the consistent estimation when either the covariance matrix of the measurement errors or the reliability matrix of independent variables is known. Their finite- and large-sample properties are derived with not necessarily normal errors. A Monte Carlo simulation is carried out to study the the finite properties of the estimators. Keywords: Consistent estimationMeasurement errorsReliability matrixStochastic linear restrictionsMathematics Subject Classification: 62F1062F12 Acknowledgments The authors would like to thank the anonymous referees for their suggestions which led to a substantially improved version of the article. This research is supported by the National Natural Science Foundation of China (no. 11171361).