The polynomial and the Poisson measurement error models: some further results on quasi score and corrected score estimation

The asymptotic covariance matrices of the corrected score, the
quasi score, and the simple score estimators of a polynomial
measurement error model have been derived in the literature. Here
some alternative formulas are presented, which might lead to an
easier computation of these matrices. In particular, new properties
of the variables $t_r$ and $\mu_r$ that constitute the estimators
are derived. In addition, the term in the formula for the
covariance matrix of the quasi score estimator stemming from the
estimation of nuisance parameters is evaluated. The same is done
for the log-linear Poisson measurement error model. In the
polynomial case, it is shown that the simple score and the quasi
score estimators are not always more efficient than the corrected
score estimator if the nuisance parameters have to be estimated.