Parameter estimation in measurement error models

In the regression model, it is assumed that the independent variable is measured without error. If this assumption is not provided, the data is corrupted by measurement errors. In data analysis, measurement errors are very common. In the presence of measurement errors in the data, the validity of classical statistical methods tends to fall, and the least squares estimators of the parameters become biased and inconsistent. In order to find consistent estimator of parameters, some additional information is required, such as the known covariance matrix of the measurement errors and the known reliability matrix. In this study, alternative parameter estimation methods in case of measurement errors in variables are considered. Moreover, some biased parameter estimation approaches to the measurement error models in case of multicollinearity in data are examined. Also, these estimators are evaluated with theoretical and numerical examples. Key Words: Measurement error model, Identifiability, Reliability matrix, Instrumental variables technique, Liu estimation approach