New weighted geometric mean method to estimate the slope of measurement error model

This paper introduces a new weighted geometric mean (WG) estimator to fit regression line when both the response and explanatory variables are subject to measurement errors. The proposed estimator is based on the mathematical relationship between the vertical and orthogonal distances of the observed points and the regression line (cf. Saqr and Khan, 2012). It minimizes the orthogonal distance of the observed points from the unfitted line. The WG estimator is less sensitive to the ratio of error variances (λ).  It is a better alternative than the currently used geometric mean (GM) and OLS-bisector estimators. Extensive simulation results show that the proposed WG estimator is much more stable than the geometric mean and OLS-bisector estimators. The mean absolute error of the WG estimator is consistently smaller than the geometric mean and OLS-bisector estimators.