Limit Theorems for the Inductive Mean on Metric Trees
Limit Theorems for the Inductive Mean on Metric Trees
复制标题
度量树上归纳均值的极限定理
DOI：
10.1239/jap/1294170525
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发表时间：
2010
影响因子：
1
通讯作者：
Bojan Basrak
中科院分区：
文献类型：
--
作者：
Bojan Basrak
对于二元度量树上的随机变量，期望值的定义可以推广到重心的概念。为了从树值数据中估计重心，使用当前均值和新数据点之间的加权插值递归地构造所谓的归纳均值。我们的归纳平均值的强一致性，而且，它，有点奇怪，收敛到真正的重心与不同的速度，渐近分布取决于小的变化的基础分布。
For random variables with values on binary metric trees, the definition of the expected value can be generalized to the notion of a barycenter. To estimate the barycenter from tree-valued data, the so-called inductive mean is constructed recursively using the weighted interpolation between the current mean and a new data point. We show the strong consistency of the inductive mean, but also that it, somewhat peculiarly, converges towards the true barycenter with different rates, and asymptotic distributions depending on the small variations of the underlying distribution.