Estimating A Polynomial Regression With Measurement Errors In The Structural And In The Functional Case - A Comparison

Two methods of estimating the parameters of a polynomial regression with measurement errors in the regressor variable are compared to each other with respect to their relative efficiency and robustness. One of the two estimators (SLS) is valid for the structural variant of the model and uses the assumption that the true regressor variable is normally distributed, while the other one (ALS and also its small sample modification MALS) does not need any assumption on the regressor distribution. SLS turns out to react rather strongly on violations of the normality assumption as far as its bias is concerned but is quite robust with respect to its MSE. It is more efficient than ALS or MALS whenever the normality assumption holds true