Moment estimation of measurement errors

Abstract

The slope of the best-fit line from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four. We use second order and fourth order moment equations to estimate the ratio of the variances of errors in the measurement error model and this estimate is used to introduce two new estimators. A simulation study shows improvement in bias and mean squared error of each of these new estimators over the ordinary least squares estimator.