This paper proposes to estimate possibly misspecified semiparametric estimating equations models using a two-step combined nonparametric likelihood method. The method uses in the first step the plug in principle and replaces the infinite dimensional parameter with a consistent estimator. In the second step an estimator for the finite dimensional parameter is obtained by combining exponential tilting with a another member of the empirical Cressie-Read discrepancy. The resulting class of semiparametric estimators are robust to misspecification and have the same asymptotic variance as that of the efficient semiparametric generalised method of moment estimator under correct specification. It is also shown that the asymptotic distributions of the proposed estimators can be consistently estimated by a multiplier bootstrap procedure. The results of the paper are illustrated with a quadratic inference function model and an instrumental variable partially linear additive model. Monte Carlo evidence suggests that the proposed estimators have competitive finite sample properties.

中文翻译：

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错误指定半参数模型的两步组合非参数似然估计

本文建议使用两步组合非参数似然方法来估计可能错误指定的半参数估计方程模型。该方法在第一步中原则上使用插件，并用一致的估计量替换无限维参数。在第二步中，通过将指数倾斜与经验 Cressie-Read 差异的另一个成员相结合，获得有限维参数的估计量。由此产生的半参数估计量对错误指定具有鲁棒性，并且具有与正确指定下的矩估计量的有效半参数广义方法相同的渐近方差。还表明，建议的估计量的渐近分布可以通过乘数引导程序一致地估计。论文的结果用二次推理函数模型和工具变量部分线性加性模型说明。蒙特卡罗证据表明，所提出的估计量具有竞争性有限样本特性。