论文标题
Fréchet的有限样品丝毫丝绸，并应用于气候
Finite Sample Smeariness of Fréchet Means and Application to Climate
论文作者
论文摘要
非欧亚人空间上的Fréchet平均值可能表现出非标准的渐近率，从而使基于分位数的渐近推理不适用。我们在这里表明，这影响了所有支撑超过半圈的圆形分布。我们详尽地描述了这一现象，并引入了一个新概念，我们称之为有限样品涂片（FSS）。在存在FSS的情况下，事实证明，基于分位数的Fréchet平等测试意味着有效水平高于其标称水平，而在I型FSS的情况下，该水平均无渐进。相比之下，合适的基于引导的测试对FSS正确，渐近地达到了正确的水平。为了说明FSS在实际数据中的相关性，我们将方法应用于来自两个欧洲城市的定向风数据。事实证明，基于分位数的测试（未校正FSS）会找到多种重要的风变化。当我们使用引导程序测试时，这种众多的凝结到几年中，以大幅变化为特征，以纠正FSS。
Fréchet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates rendering quantile-based asymptotic inference inapplicable. We show here that this affects, among others, all circular distributions whose support exceeds a half circle. We exhaustively describe this phenomenon and introduce a new concept which we call finite samples smeariness (FSS). In the presence of FSS, it turns out that quantile-based tests for equality of Fréchet means systematically feature effective levels higher than their nominal level which perseveres asymptotically in case of Type I FSS. In contrast, suitable bootstrap-based tests correct for FSS and asymptotically attain the correct level. For illustration of the relevance of FSS in real data, we apply our method to directional wind data from two European cities. It turns out that quantile based tests, not correcting for FSS, find a multitude of significant wind changes. This multitude condenses to a few years featuring significant wind changes, when our bootstrap tests are applied, correcting for FSS.
