论文标题
一种灵活的方法，用于正常近似几何和拓扑统计
A Flexible Approach for Normal Approximation of Geometric and Topological Statistics
论文作者
论文摘要
我们得出了一类二项式或泊松点过程的稳定功能的正常近似结果，这些功能不一定作为某些得分函数的总和表达。我们的方法是基于附加成本运营商的灵活概念，该概念有助于通过适当适当的一阶操作员来处理二阶成本运营商。我们将这种灵活的概念与强稳定理论结合在一起，以建立我们的结果。我们通过在实践中经常出现的某些几何和拓扑统计数据来建立正常的近似结果来说明结果的适用性。现有结果也出现为我们方法的特殊情况。
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the add-one cost operator, which helps one to deal with the second-order cost operator via suitably appropriate first-order operators. We combine this flexible notion with the theory of strong stabilization to establish our results. We illustrate the applicability of our results by establishing normal approximation results for certain geometric and topological statistics arising frequently in practice. Several existing results also emerge as special cases of our approach.
