Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices
Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices
复制标题
DOI：
10.1007/s11749-009-0168-4
复制
发表时间：
2010-08-01
期刊：
影响因子：
1.3
通讯作者：
Duong, T.
中科院分区：
文献类型：
--
作者：
Chacon, J. E.;Duong, T.
多元核密度估计是探索性数据分析中的一项重要技术。它的实用性依赖于它的易解性，特别是通过图形手段。决定核密度估计性能的关键因素是带宽矩阵的选择。寻找最佳带宽矩阵的研究始于模拟单变量选择器的带宽矩阵的受限参数化。这些限制逐渐放松，以开发出更灵活的选择器。在这篇文章中，我们提出了第一个插入式带宽选择器，它具有最终选择器和导频选择器的无约束参数。到目前为止，传统的高阶导数矢量化阻碍了无约束导频选择器的发展，导致矩阵代数表达式变得越来越难处理。我们通过引入另一种矢量化来解决这个问题，它给出了优雅和易处理的表达式。这使我们能够量化无约束导频选择器的渐近和有限样本性质。对于结构复杂的目标密度(如多通道)，我们的无约束选择器比现有的插件选择器显示出最大的改进。
Multivariate kernel density estimation is an important technique in exploratory data analysis. Its utility relies on its ease of interpretation, especially by graphical means. The crucial factor which determines the performance of kernel density estimation is the bandwidth matrix selection. Research in finding optimal bandwidth matrices began with restricted parameterizations of the bandwidth matrix which mimic univariate selectors. Progressively these restrictions were relaxed to develop more flexible selectors. In this paper, we propose the first plug-in bandwidth selector with the unconstrained parameterizations of both the final and pilot selectors. Up till now, the development of unconstrained pilot selectors was hindered by the traditional vectorization of higher-order derivatives which lead to increasingly intractable matrix algebraic expressions. We resolve this by introducing an alternative vectorization which gives elegant and tractable expressions. This allows us to quantify the asymptotic and finite sample properties of unconstrained pilot selectors. For target densities with intricate structure (such as multimodality), our unconstrained selectors show the most improvement over the existing plug-in selectors.