ADAPTIVE AND MINIMAX ESTIMATION OF THE CUMULATIVE DISTRIBUTION FUNCTION GIVEN A FUNCTIONAL COVARIATE
ADAPTIVE AND MINIMAX ESTIMATION OF THE CUMULATIVE DISTRIBUTION FUNCTION GIVEN A FUNCTIONAL COVARIATE
复制标题
给定函数协变量的累积分布函数的自适应和极小极大估计
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Roche
中科院分区：
文献类型：
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作者：
G. Chagny;A. Roche
考虑了在函数协变量下条件累积分布函数的非参数核估计。鉴于风险的偏差-方差权衡，我们首先本着最近的Goldenshluger-Lepski方法和模型选择工具的精神，提出了一种完全数据驱动的带宽选择设备。由此产生的估计是自适应和最小最大最优：我们建立非渐近风险界和计算速度的收敛性在各种假设下的小球概率的函数变量的衰减。我们还证明了下界。两个逐点和集成的标准被认为是。最后，还讨论了估计量定义中所涉及的范数或半范数的选择，以及数据在有限维子空间上的投影。数值结果说明了该方法。
We consider the nonparametric kernel estimation of the conditional cumulative distribution function given a functional covariate. Given the bias-variance trade-off of the risk, we first propose a totally data-driven bandwidth selection device in the spirit of the recent Goldenshluger-Lepski method and of model selection tools. The resulting estimator is shown to be adaptive and minimax optimal: we establish nonasymptotic risk bounds and compute rates of convergence under various assumptions on the decay of the small ball probability of the functional variable. We also prove lower bounds. Both pointwise and integrated criteria are considered. Finally, the choice of the norm or semi-norm involved in the definition of the estimator is also discussed, as well as the projection of the data on finite dimensional subspaces. Numerical results illustrate the method.
影响因子：
4.5
作者：
Crambes, Christophe;Kneip, Alois;Sarda, Pascal
通讯作者：
Sarda, Pascal