Adaptive minimax density estimation on ℝ d for Huber’s contamination model
Adaptive minimax density estimation on ℝ d for Huber’s contamination model
复制标题
Huber 污染模型对 d 的自适应极小极大密度估计
DOI：
10.1093/imaiai/iaad045
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Ren, Zhao
中科院分区：
文献类型：
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作者：
Zhang, Peiliang;Ren, Zhao
研究了Huber污染模型下带损失函数的自适应Minimax密度估计问题.为了研究污染对密度最优估计的影响，我们首先假设密度是各向异性的Nikol'skii类，建立Minimax率。然后，我们开发了一个数据驱动的核估计，这可以被视为一个强大的推广的Goldenshluger-Lepski方法的带宽选择过程。我们表明，建议的带宽选择规则可以导致估计是极小极大自适应的平滑参数或污染的比例。当这两个都是未知的，我们证明了找到任何最小最大速率自适应方法是不可能的。扩展到顺利污染的情况下也进行了讨论。
We address the problem of adaptive minimax density estimation onwithloss functions under Huber’s contamination model. To investigate the contamination effect on the optimal estimation of the density, we first establish the minimax rate with the assumption that the density is in an anisotropic Nikol’skii class. We then develop a data-driven bandwidth selection procedure for kernel estimators, which can be viewed as a robust generalization of the Goldenshluger-Lepski method. We show that the proposed bandwidth selection rule can lead to the estimator being minimax adaptive to either the smoothness parameter or the contamination proportion. When both of them are unknown, we prove that finding any minimax-rate adaptive method is impossible. Extensions to smooth contamination cases are also discussed.