论文标题
抽象空间中深度度量的水平集
Level sets of depth measures in abstract spaces
论文作者
论文摘要
一个点的镜头深度已扩展到通用度量空间，大多数深度都不是这种情况。它被定义为在两个随机点x和y的两个随机球的交点中包含的概率，而半径d（x，y）相同。我们基于一般度量空间上的IID样本研究了Hausdorff和测量距离的一致性。我们还证明，经验水平集的边界是其人口对应物的一致估计值，并分析了两个现实生活中的例子
The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y, with the same radius d(X, Y). We study the consistency in Hausdorff and measure distance, of the level sets of the empirical lens depth, based on an iid sample on a general metric space. We also prove that the boundary of the empirical level sets are consistent estimators of their population counterparts, and analyze two real-life examples
