Voronoi强度估计的重采样平滑
Resample-smoothing of Voronoi intensity estimators
摘要：
Voronoi强度估计，这是点过程的强度函数的非参数估计，都是无参数和自适应的，在一个给定的位置的强度估计是由包含该位置的Voronoi/Dirichlet细胞的倒数大小。然而，它们的主要缺点是，它们倾向于在观察到的点图案的点密度高的区域中使数据欠平滑，而在点密度低的区域中使数据过平滑。为了解决这个问题，即找到一些中间地带之间的过度和欠平滑，我们提出了一个额外的平滑技术的Voronoi强度估计的点过程在任意度量空间，这是基于重复的独立稀疏的点过程/模式。通过模拟研究，我们表明，我们的重采样平滑技术，提高了估计显着。此外，我们还研究了无偏性和方差等统计特性，并提出了一种经验法则和数据驱动的交叉验证方法来选择要应用的细化/平滑量。最后，我们将我们提出的强度估计方案应用于两个数据集：松树树苗的位置（平面点模式）和机动车交通事故（线性网络点模式）。
英文摘要：
Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the Voronoi/Dirichlet cell containing that location. Their major drawback, however, is that they tend to under-smooth the data in regions where the point density of the observed point pattern is high and over-smooth in regions where the point density is low. To remedy this problem, i.e. to find some middle-ground between over- and under-smoothing, we propose an additional smoothing technique for Voronoi intensity estimators for point processes in arbitrary metric spaces, which is based on repeated independent thinnings of the point process/pattern. Through a simulation study we show that our resample-smoothing technique improves the estimation significantly. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of thinning/smoothing to apply. We finally apply our proposed intensity estimation scheme to two datasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern).
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