STICKY CENTRAL LIMIT THEOREMS ON OPEN BOOKS
STICKY CENTRAL LIMIT THEOREMS ON OPEN BOOKS
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DOI：
10.1214/12-aap899
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发表时间：
2013-12-01
影响因子：
1.8
通讯作者：
Skwerer, Sean
中科院分区：
文献类型：
--
作者：
Hotz, Thomas;Huckemann, Stephan;Skwerer, Sean
给定一本打开的书上的概率分布（通过沿其边界超平面粘合半空间副本的不相交并得到的度量空间），我们定义了Frechet平均值（重心）粘滞的精确概念。这种非经典现象被大数定律（LLN）量化，该定律表明经验平均值最终几乎肯定位于胶合超平面（余维为1，因此测量值为0）脊柱上，中心极限定理（CLT）表明极限分布是高斯分布并支持脊柱上。我们还针对平均值为非粘性（即，不在脊柱上）和部分粘性（即，在脊柱上但不粘性）的情况说明了LLN和CLT的版本。
Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Frechet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine. We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky).