论文标题
Hellinger-bhattacharyya跨验验，用于保存形状的多元小波阈值
Hellinger-Bhattacharyya cross-validation for shape-preserving multivariate wavelet thresholding
论文作者
论文摘要
小波方法对密度估计的好处在文献中已经很好地确定，尤其是当估计的密度在平稳性上是不规则或异质性的时。但是，小波密度估计通常不是真正的密度。在Aya-Moreno等人（2018年）中，引入了“形状的”小波密度估计器，包括作为密度方形 - 根根的主要步骤。涉及密度平方根的自然概念是地狱般的距离 - 或等效地，bhattacharyya亲和力系数。在本文中，我们通过优化Hellinger-Bhattacharyya Criterion的原始保留版本来选择所有用户定义的参数（例如分辨率级别或阈值规格）的全部数据驱动版本。建立了所提出的程序的理论最优性，而模拟显示了估计器的强大实践性能。在该框架内，我们还提出了一种新颖但自然的“折刀阈值”方案，该方案优于其他更古典的阈值选项。
The benefits of the wavelet approach for density estimation are well established in the literature, especially when the density to estimate is irregular or heterogeneous in smoothness. However, wavelet density estimates are typically not bona fide densities. In Aya-Moreno et al (2018), a `shape-preserving' wavelet density estimator was introduced, including as main step the estimation of the square-root of the density. A natural concept involving square-root of densities is the Hellinger distance - or equivalently, the Bhattacharyya affinity coefficient. In this paper, we deliver a fully data-driven version of the above 'shape-preserving' wavelet density estimator, where all user-defined parameters, such as resolution level or thresholding specifications, are selected by optimising an original leave-one-out version of the Hellinger-Bhattacharyya criterion. The theoretical optimality of the proposed procedure is established, while simulations show the strong practical performance of the estimator. Within that framework, we also propose a novel but natural 'jackknife thresholding' scheme, which proves superior to other, more classical thresholding options.
