Nonparametric inference for Poisson‐Laguerre tessellations
研究了泊松-拉盖尔镶嵌的统计推断，提出了两个非参数估计量来估计生成点到达时间的分布函数，并证明了其强相合性，适用于观察窗口无限扩大的情况。
Abstract In this paper, we consider statistical inference for Poisson‐Laguerre tessellations in . The object of interest is a distribution function which describes the distribution of the arrival times of the generator points. The function uniquely determines the intensity measure of the underlying Poisson process. Two nonparametric estimators for are introduced, which depend only on the points of the Poisson process that generate non‐empty cells and the actual cells corresponding to these points. The proposed estimators are proven to be strongly consistent as the observation window expands unboundedly to the whole space. We also consider a stereological setting, where one is interested in estimating the distribution function associated with the Poisson process of a higher‐dimensional Poisson‐Laguerre tessellation, given that a corresponding sectional Poisson‐Laguerre tessellation is observed.