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