MINIMAX ESTIMATION OF A FUNCTIONAL ON A STRUCTURED HIGH-DIMENSIONAL MODEL
MINIMAX ESTIMATION OF A FUNCTIONAL ON A STRUCTURED HIGH-DIMENSIONAL MODEL
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DOI：
10.1214/16-aos1515
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发表时间：
2017-10-01
影响因子：
4.5
通讯作者：
van der Vaart, Aad
中科院分区：
文献类型：
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作者：
Robins, James M.;Li, Lingling;van der Vaart, Aad
介绍了半参数模型和非参数模型参数估计的一种新方法。该方法使用基于感兴趣参数的高阶影响函数的U-统计量，该U-统计量扩展了普通的线性影响函数，并表示该参数的高阶导数。对于不能完美表示的参数，该方法经常导致偏差-方差权衡，并导致估计器以比根n率更慢的速度收敛。在许多例子中，所得到的速率可以被证明是最佳的。我们特别感兴趣的是在具有高维或低正则参数的滋扰参数模型中的参数估计，其中感兴趣的参数不能以根n-率估计，但我们也考虑使用新的非线性估计器进行有效的根n-估计。将一般方法详细地应用于估计不总是观察到的响应时的平均响应的例子。
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method employs U-statistics that are based on higher-order influence functions of the parameter of interest, which extend ordinary linear influence functions, and represent higher derivatives of this parameter. For parameters for which the representation cannot be perfect the method often leads to a bias-variance trade-off, and results in estimators that converge at a slower thanv root n-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 root n-rate, but we also consider efficient root n-estimation using novel nonlinear estimators. The general approach is applied in detail to the example of estimating a mean response when the response is not always observed.