We observe a realization of a stationary weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling technique to construct an unbiased estimator of the average value of this geometric characteristic. Under mild conditions on the weights of the cells, we establish variance asymptotics and the asymptotic normality of the unbiased estimator as the observation window tends to the whole space. Moreover, weak consistency is shown for this estimator.

中文翻译：

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随机镶嵌统计无偏和一致估计量的极限理论

我们观察到一个固定加权 Voronoi 镶嵌的实现d有界观察窗口内的维欧几里得空间。给定典型细胞的几何特征，我们使用负采样技术来构造该几何特征平均值的无偏估计量。在细胞权重的温和条件下，我们建立方差渐近和无偏估计量的渐近正态性，因为观察窗口趋向于整个空间。此外，该估计量显示出弱一致性。