Cumulants and Partition Lattices
Cumulants and Partition Lattices
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累积量和划分格
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
P. McCullagh
中科院分区：
文献类型：
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作者：
P. McCullagh
这是统计文献中第一篇指出划分格在统计矩及其近亲累积量理论中重要性的论文。在我在帝国理工学院就用图论术语表达的列昂诺夫-希里亚耶夫结果发表演讲后不久，苏珊·威尔逊首先引起了我的注意。斯皮德的论文刚出版不久，是在我通过与奥利弗·普雷策尔的谈话第一次熟悉隔断格子之后一两天到达的。自然地，我比平时更加注重细节地阅读这篇论文，因为我仍然不熟悉 Rota [18]，而且因为立即清楚了分区格子 \({\mathcal{E}}_{n}\) 上的莫比乌斯反演，按子分区部分排序，导致了清晰的证明和极大的简化。这是一篇简短的论文，但却蕴含着巨大的冲击力，对我来说，它的出现恰逢其时。
This is the first paper to appear in the statistical literature pointing out the importance of the partition lattice in the theory of statistical moments and their close cousins, the cumulants. The paper was first brought to my attention by Susan Wilson, shortly after I had given a talk at Imperial College on the Leonov-Shiryaev result expressed in graph-theoretic terms. Speed’s paper was hot off the press, arriving a day or two after I had first become acquainted with the partition lattice from conversations with Oliver Pretzel. Naturally, I read the paper with more than usual attention to detail because I was still unfamiliar with Rota [18], and because it was immediately clear that Mobius inversion on the partition lattice \({\mathcal{E}}_{n}\), partially ordered by sub-partition, led to clear proofs and great simplification. It was a short paper packing a big punch, and for me it could not have arrived at a more opportune moment.