Least Squares and Grouping Method Estimators in the Errors in Variables Model

Abstract The probability density function of the least squares estimator of the slope coefficient in the errors in variables model is presented. It is shown how the bias and mean-square error of the least squares estimator b depend on the parameters of the model. In particular, for a given sample size, b converges to the true parameter as one of the distribution parameters increases indefinitely. The analysis is supplemented with numerical computations of the relative bias and mean-square error. The distribution function of the grouping method estimator has the same form as that of 6. The biases and mean-square errors of b and are compared. For the case of zero within-group variance, the use of always reduces the magnitude of the relative bias and generally reduces the mean-square error. For large values of the within-group variance, use of may result in an increase in mean-square error.