  This paper proposes a closed-form optimal estimator based on the theory of
estimating functions for a class of linear ARCH models. The estimating function
(EF) estimator has the advantage over the widely used maximum likelihood (ML)
and quasi-maximum likelihood (QML) estimators that (i) it can be easily
implemented, (ii) it does not depend on a distributional assumption for the
innovation, and (iii) it does not require the use of any numerical optimization
procedures or the choice of initial values of the conditional variance
equation. In the case of normality, the asymptotic distribution of the ML and
QML estimators naturally turn out to be identical and, hence, coincides with
ours. Moreover, a robustness property of the EF estimator is derived by means
of influence function. Simulation results show that the efficiency benefits of
our estimator relative to the ML and QML estimators are substantial for some
ARCH innovation distributions.
