Estimation of slope for measurement error model with equation error: Applications on serum kanamycin data

This paper introduces a statistical method to estimate the parameters of bivariate structural errors- in-variables model (EIV). It is a complex problem when there is no or uncertain prior knowledge of the measurement errors variances. The proposed estimators of the parameters of EIV model are derived based on mathematical modication method for observed data. This method is suggested to reproduce an explanatory variable that has equivalent statistical characteristics of the unobserved explanatory vari- able, and to correct for the effects of measurement error in predictors. The proposed method produce robust estimators, and it is straightforward, easy to implement, and takes into account the equation errors. The simulation studies show that the new estimator to be generally more efficient and less biased than some other previous approaches. Compared to the maximum likelihood method via the simulation studies, the estimators of the proposed method are nearly asymptotically unbiased and efficient when there is no or uncertain prior knowledge of the measurement errors variances. The numerical comparisons of the simulation studies results are included.In addition, results are illustrated with applications on one well-known real data sets of serum kanamycin.