Quasi Score is more efficient than Corrected Score in a polynomial measurement error model. Discussion Paper 445/SFB 386, Universität München

We consider a polynomial regression model, where the covariate is measured with Gaussian errors. The measurement error variance is supposed to be known. The covariate is normally distributed with known mean and vari-ance. Quasi Score (QS) and Corrected Score (CS) are two consistent estima-tion methods, where the first makes use of the distribution of the covariate (structural method), while the latter does not (functional method). It may therefore be surmised that the former method is (asymptotically) more ef-ficient than the latter one. This can, indeed, be proved for the regression parameters. We do this by introducing a third, so-called Simple Score (SS), estimator, the efficiency of which turns out to be intermediate between QS and CS. When one includes structural and functional estimators for the vari-ance of the error in the equation, SS is still more efficient than CS. When the mean and variance of the covariate are not known and have to be esti-mated as well, one can still maintain that QS is more efficient than SS for the regression parameters