Regression with Errors in the Variables

Abstract An adjusted least squares estimator introduced by Cheng and Schneeweiss for consistently estimating a polynomial regression of any degree with errors in the variables is modi ed such that it shows good results in small samples without losing its asymptotic properties for large samples Simulation studies corroborate the theoretical ndings The new method is applied to analyse a geophysical law relating the depth of earthquakes to their distance from a trench where one of the earths plates is submerged beneath another one Keywords Polynomial regression measurement error adjusted least squares modi ed adjusted least squares small sample properties Cheng and Schneeweiss hereafter CS building on the work of Chan and Mak and Stefanski developed a consistent estimator of the parameters of a polynomial regression with errors in the variable