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首页> 外文期刊>Journal of applied statistics >Le Cam theorem on interval division by randomly chosen points: Pedagogical explanations and application to temporal cluster detection
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Le Cam theorem on interval division by randomly chosen points: Pedagogical explanations and application to temporal cluster detection

机译：随机选择点的区间除法的Le Cam定理：教学论解释及其在时态聚类检测中的应用

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The aim of this paper is to propose a pedagogical explanation of the Le Cam theorem and to illustrate its use, through a practical application, for temporal cluster detection. This theorem focusses on the interval division by randomly chosen points. The aim of the theorem is to characterize the asymptotic behavior of a certain category of sums of functions applied to the length of successive intervals between points. It is not very intuitive and its understanding needs some deepening. After enouncing the theorem, its different aspects are explained and detailed in a way as pedagogical as possible. Theoretical applications are proposed through the proof of two propositions. Then a very concrete application of this theorem for temporal cluster detection is presented, tested by a power study, and compared with other global cluster detection tests. Finally, this approach is applied to the well-known Knox temporal data set.
机译：本文的目的是提出Le Cam定理的教学解释，并通过实际应用说明其在时间聚类检测中的用途。该定理集中于间隔除以随机选择的点。该定理的目的是表征应用于点之间连续间隔长度的函数和的特定类别的渐近行为。它不是很直观，需要加深对它的理解。宣布该定理后，将以尽可能多的教学方式解释和详细说明其不同方面。通过两个命题的证明，提出了理论应用。然后，提出了该定理在时间集群检测中的一个非常具体的应用，通过幂研究进行了测试，并与其他全局集群检测测试进行了比较。最后，此方法应用于众所周知的Knox时间数据集。

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