A Comparison of Asymptotic Covariance Matrices of Adjusted Least Squares and Structural Least Squares in Error Ridden Polynomial Regression

A polynomial structural errors-in-variables model with normal
underlying distributions is investigated. An asymptotic covariance
matrix of the SLS estimator is computed, including the correcting
terms which appear because in the score function the sample mean
and the sample variance are plugged in. The ALS estimator is also
considered, which does not need any assumption on the regressor
distribution. The asymptotic covariance matrices of the two
estimators are compared in border cases of small and of large
errors. In both situations it turns out that under the normality
assumption SLS is strictly more efficient than ALS.