Quasi Score is more efficient than Corrected Score in a general nonlinear measurement error model

We compare two consistent estimators of the parameter vector beta
of a general exponential family measurement error model with
respect to their relative efficiency. The quasi score (QS)
estimator uses the distribution of the regressor, the corrected
score (CS) estimator does not make use of this distribution and is
therefore more robust. However, if the regressor distribution is
known, QS is asymptotically more efficient than CS. In some cases
it is, in fact, even strictly more efficient, in the sense that the
difference of the asymptotic covariance matrices of CS and QS is
positive definite.