论文标题
统计分析非凸度的度量
Statistical analysis of measures of non-convexity
论文作者
论文摘要
文献中引入了几种非跨性别度（偏离凸度）的方法，包括集合和功能。其中一些具有几何性质，而另一些则具有拓扑性质。我们通过基于$ S $中的点样本来处理其估算，以解决集合$ S $的非凸度的统计分析。我们还引入了一种新的非凸度度量。我们简要讨论了这些不同的非跨性别概念，证明一致性并为提出的估计量找到渐近分布。我们还考虑了这些估计器的实际实施，并说明了它们对真实数据示例的适用性。
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical analysis of some of these measures of non-convexity of a set $S$, by dealing with their estimation based on a sample of points in $S$. We introduce also a new measure of non-convexity. We discuss briefly about these different notions of non-convexity, prove consistency and find the asymptotic distribution for the proposed estimators. We also consider the practical implementation of these estimators and illustrate their applicability to a real data example.
