A Small Sample Estimator for a Polynomial Regression with Errors in the Variables

Abstract

An adjusted least squares estimator, introduced by Cheng and Schneeweiss (1998) for consistently estimating a polynomial regression of any degree with errors in the variables, is modified such that it shows good resutls in small samples without losing its asymptotic properties for large samples. Simulation studies corroborate the theoretical findings. 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 earth's plates is submerged beneath another one. (This is joint work with Chi-Lun Cheng and Markus Thamerus).