A Review and Some New Proposals for Bandwidth Selection in Nonparametric Density Estimation for Dependent Data
A Review and Some New Proposals for Bandwidth Selection in Nonparametric Density Estimation for Dependent Data
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相关数据非参数密度估计中带宽选择的回顾和一些新建议
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
R. Cao
中科院分区：
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作者：
Inés Barbeito;R. Cao
在假设独立性的情况下，密度估计中平滑参数的选择问题已经得到了广泛的研究。然而，在考虑依赖性时，很少有论文涉及数据驱动的带宽选择器。首先，我们回顾了现有的带宽选择相关的方法的最新进展。此外，三个新（或适应）的方法提出：（a）一个扩展的依赖情况下的修改交叉验证的Stute（J Statisti Plann Infer 30：293-305，1992; B）Estevez-Perez等人提出的惩罚交叉验证的密度估计的适应。（J Statisti Plann Infer 104：1-30，2002）用于危险率估计;（c）最后，建立了所谓的移动块自助法的平滑形式，并在此基础上得到了相关条件下的均方误差的自助形式的精确表达式。这是有用的，因为不需要Monte Carlo近似来实现引导选择器。为了检查和比较六个选定的带宽的经验行为进行了广泛的模拟研究。
When assuming independence, the choice of the smoothing parameter in density estimation has been extensively studied. However, when considering dependence, very few papers have dealt with data-driven bandwidth selectors. First of all, we review the state of art of the existing methods for bandwidth selection under dependence. Moreover, three new (or adapted) methods are proposed: (a) an extension to the dependent case of the modified cross-validation by Stute (J Statisti Plann Infer 30:293–305, 1992; b) an adaptation to density estimation of the penalized cross-validation proposed by Estevez-Perez et al. (J Statisti Plann Infer 104:1–30, 2002) for hazard rate estimation; (c) finally, the smoothed version of the so-called moving blocks bootstrap is established and an exact expression for the bootstrap version of the mean integrated squared error under dependence is obtained in this context. This is useful since Monte Carlo approximation is not needed to implement the bootstrap selector. An extensive simulation study is carried out in order to check and compare the empirical behaviour of six selected bandwidths.