论文标题
几何概率统计量的总变化正常近似
Normal approximation in total variation for statistics in geometric probability
论文作者
论文摘要
我们使用Stein的方法来确定大量分数泊松点过程的总变化距离的速率，以$ \ Mathbb {r}^d $上的分数poisson点过程。就像在较弱的kolmogorov距离下的研究中一样，假定得分函数可以满足稳定和矩条的满足。以进一步的分数功能为代价，我们表明速率与Kolmogorov距离下的速率一致。我们演示了定理在四个应用程序中的使用：voronoi tessellation，$ k $ - 最近的邻居，木材体积和最大层。
We use Stein's method to establish the rates of normal approximation in terms of the total variation distance for a large class of sums of score functions of marked Poisson point processes on $\mathbb{R}^d$. As in the study under the weaker Kolmogorov distance, the score functions are assumed to satisfy stabilizing and moment conditions. At the cost of an additional non-singularity condition for score functions, we show that the rates are in line with those under the Kolmogorov distance. We demonstrate the use of the theorems in four applications: Voronoi tessellation, $k$-nearest neighbours, timber volume and maximal layers.
