Robins James, Li Lingling, Tchetgen Eric, van der Vaart Aad W
Department of Biostatistics and Epidemiology, School of Public Health, Harvard University, Cambridge, USA.
Metrika. 2009 Mar;69(2-3):227-247. doi: 10.1007/s00184-008-0214-3.
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.
我们讨论了一种用于估计半参数和非参数模型中参数的新方法。该方法基于由二次影响函数构造的U统计量。后者扩展了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，该方法导致偏差 - 方差权衡，并产生收敛速度慢于n^(-1/2)速率的估计量。在许多示例中，可以证明所得速率是最优的。我们特别感兴趣的是估计具有高维或低正则性干扰参数的模型中的参数，其中感兴趣的参数不能以n^(-1/2)速率进行估计。
