We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n−1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n−1/2-rate.

中文翻译：

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二次半参数 Von Mises 演算

我们讨论了一种在半参数和非参数模型中估计参数的新方法。该方法基于由二次影响函数构建的 U 统计量。后者扩展了在半参数理论中定义的感兴趣参数的普通线性影响函数，并表示该参数的二阶导数。对于匹配不能完美的参数，该方法会导致偏差-方差权衡，并导致估计器以比 n-1/2 速率慢的速度收敛。在许多示例中，结果速率可以被证明是最佳的。我们对在具有高维度或低规律性的有害参数的模型中估计参数特别感兴趣，其中感兴趣的参数不能以 n-1/2 速率进行估计。