Kukush, Alexander and Schneeweiß, Hans and Wolf, R.
Comparison of three estimators in a polynomial regression with measurement errors.
Collaborative Research Center 386, Discussion Paper 233
In a polynomial regression with measurement errors in the covariate, which is supposed to be normally distributed, one has (at least) three ways to estimate the unknown regression parameters: one can apply ordinary least squares (OLS) to the model without regard of the measurement error or one can correct for the measurement error, either by correcting the estimating equation (ALS) or by correcting the mean and variance functions of the dependent variable, which is done by conditioning on the observable, error ridden, counter part of the covariate (SLS). While OLS is biased the other two estimators are consistent. Their asymptotic covariance matrices can be compared to each other, in particular for the case of a small measurement error variance.