It is well known, that Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates depending on curvature. Even for distributions featuring standard asymptotic rates, there are non-Euclidean effects, altering finite sampling rates up to considerable sample sizes. These effects can be measured by the variance modulation function proposed by Pennec (2019). Among others, in view of statistical inference, it is important to bound this function on intervals of sampling sizes. In a first step into this direction, for the special case of a K-spider we give such an interval, based only on folded moments and total probabilities of spider legs and illustrate the method by simulations.

翻译：众所周知，非欧空间上的弗雷歇均值可能因曲率不同而呈现非标准渐近速率。即使对于具有标准渐近速率的分布，也存在非欧效应，直至相当大的样本量时仍会改变有限采样速率。这些效应可通过Pennec（2019）提出的方差调制函数进行度量。在统计推断等应用中，界定该函数在采样规模区间上的取值至关重要。作为该研究方向的第一步，我们针对K-蛛网这一特例，仅基于蛛网腿的折叠矩与总概率给出了此类区间，并通过模拟验证了该方法。