论文标题
泊松船体
Poisson hulls
论文作者
论文摘要
我们在泊松点过程中介绍了一个船体操作员，最简单的例子是欧几里得空间中点过程支持的凸壳。假设该过程的强度度量是在船体操作员生成的集合中知道的，我们将讨论对托管过程中构建的预期线性统计量的估计。在特殊情况下，我们的一般方案产生了凸体的体积或Hölder函数积分不可或缺的估计器的估计器。我们表明，估计误差是由Kabanov--Skorohod积分在基础泊松过程中给出的。我们方法的关键要素是基础泊松过程相对于船体的空间强摩托马夫。我们得出了估计误差的正常收敛速率，并将其在应用到Hölder函数积分估计器的应用中说明。我们还讨论了高阶对称统计数据的估计。
We introduce a hull operator on Poisson point processes, the easiest example being the convex hull of the support of a point process in Euclidean space. Assuming that the intensity measure of the process is known on the set generated by the hull operator, we discuss estimation of an expected linear statistic built on the Poisson process. In special cases, our general scheme yields an estimator of the volume of a convex body or an estimator of an integral of a Hölder function. We show that the estimation error is given by the Kabanov--Skorohod integral with respect to the underlying Poisson process. A crucial ingredient of our approach is a spatial strong Markov property of the underlying Poisson process with respect to the hull. We derive the rate of normal convergence for the estimation error, and illustrate it on an application to estimators of integrals of a Hölder function. We also discuss estimation of higher order symmetric statistics.
