论文标题
定向最高密度区域的非参数估计
Nonparametric estimation of directional highest density regions
论文作者
论文摘要
从与之密切相关的点样本中重建集的集合是集估计理论的目标。在这种情况下，一个特定的问题是与密度级别集的重建相关的问题，特别是那些具有高概率内容（即最高密度区域）的问题。 我们根据内核平滑定义了定向数据的最高密度区域，并提供了插入式估计器。为提案的实际实施提供了合适的引导带宽选择器。一项广泛的仿真研究表明，插入式估计器的性能与Bootstrap带宽选择器以及针对圆形和球形内核密度估计的其他带宽选择器的性能。该方法用于分析动物取向和地震学中的两个实际数据集。
Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and specifically, those ones with a high probability content, namely highest density regions. We define highest density regions for directional data and provide a plug-in estimator, based on kernel smoothing. A suitable bootstrap bandwidth selector is provided for the practical implementation of the proposal. An extensive simulation study shows the performance of the plug-in estimator proposed with the bootstrap bandwidth selector and with other bandwidth selectors specifically designed for circular and spherical kernel density estimation. The methodology is applied to analyze two real data sets in animal orientation and seismology.
