Optimality of the quasi-score estimator in a mean-variance model with applications to measurement error models

Optimality of the quasi-score estimator in a mean-variance model with applications to measurement error models

Beschreibung

vor 18 Jahren
We consider a regression of $y$ on $x$ given by a pair of mean and
variance functions with a parameter vector $\theta$ to be estimated
that also appears in the distribution of the regressor variable
$x$. The estimation of $\theta$ is based on an extended quasi score
(QS) function. We show that the QS estimator is optimal within a
wide class of estimators based on linear-in-$y$ unbiased estimating
functions. Of special interest is the case where the distribution
of $x$ depends only on a subvector $\alpha$ of $\theta$, which may
be considered a nuisance parameter. In general, $\alpha$ must be
estimated simultaneously together with the rest of $\theta$, but
there are cases where $\alpha$ can be pre-estimated. A major
application of this model is the classical measurement error model,
where the corrected score (CS) estimator is an alternative to the
QS estimator. We derive conditions under which the QS estimator is
strictly more efficient than the CS estimator.We also study a
number of special measurement error models in greater detail.

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