Adaptive density estimation using the blockwise Stein method
Adaptive density estimation using the blockwise Stein method
复制标题
使用块式 Stein 方法进行自适应密度估计
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. I. R. Igollet
中科院分区：
文献类型：
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作者：
P. I. R. Igollet
研究了L2（R）中未知光滑性概率密度的非参数估计问题。在傅立叶域中表示均方误差（MISE），我们表明，它是接近高斯序列模型中的均方误差。然后应用Stein的分块方法的一个改进形式，得到了一个线性单调预言不等式.这个预言不等式的两个后果是，建议的估计是尖锐的极小极大自适应范围内的Sobolev类的密度，其MISE是渐近小于或等于核密度估计与任何带宽的内核属于一个大类的功能，包括许多标准的内核。
We study the problem of nonparametric estimation of a probability density of unknown smoothness in L2(R). Expressing mean integrated squared error (MISE) in the Fourier domain, we show that it is close to mean squared error in the Gaussian sequence model. Then applying a modified version of Stein’s blockwise method, we obtain a linear monotone oracle inequality. Two consequences of this oracle inequality are that the proposed estimator is sharp minimax adaptive over a scale of Sobolev classes of densities, and that its MISE is asymptotically smaller than or equal to that of kernel density estimators with any bandwidth provided that the kernel belongs to a large class of functions including many standard kernels.