标题： ARCH模型中估计量的效率和影响函数 显示英文标题

标题： Efficiency and influence function of estimators for ARCH models

摘要： 本文基于估计函数理论提出了一类线性ARCH模型的闭式最优估计量。 与广泛应用的最大似然（ML）和准最大似然（QML）估计量相比，估计函数（EF）估计量具有以下优势：(i) 它易于实现；(ii) 它不依赖于创新项的分布假设；(iii) 它不需要使用任何数值优化程序或条件方差方程初始值的选择。 在正态性情况下，ML 和 QML 估计量的渐近分布自然相同，并且与我们的估计量一致。 此外，通过影响函数导出了 EF 估计量的稳健性性质。 仿真结果显示，对于某些ARCH创新分布，我们的估计量相对于ML和QML估计量的效率优势显著。 显示英文摘要

摘要： 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.