发表机构
Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出圆上c样本齐性检验的统一框架，包含Anderson-Darling型及基于softmax和Poisson核的新检验，理论推导渐近性质，模拟验证功效，并应用于北极熊哺乳模式分析。
AI 中文摘要
我们为圆上的 $c$ 样本齐性检验建立了一个统一框架。所提出的 $c$ 样本 Sobolev 检验类推广了基于均匀得分的两样本 Sobolev 检验，并将现有的多样本检验作为特例包含在内。我们进一步将该类嵌入到一个更广泛的聚合框架中，在该框架中，样本级 Sobolev 分量通过一般合并函数（包括平均型、最大型和插值型族）进行组合。在此类中，我们引入了首个针对圆形数据的 Anderson-Darling 型齐性检验，并进一步提出了两种旨在检测齐性多模态偏离的新检验，它们分别由 softmax 核和 Poisson 核构造。我们推导了该类的渐近零分布，证明了其对广泛固定备择假设的一致性，并获得了在平移型局部备择假设下的渐近分布。这些检验是分布自由的，因此不需要重采样。一项全面的模拟研究证明了 Anderson-Darling 型检验在多种场景下与 Cramér-von Mises 型竞争者相比具有强大的功效，以及 softmax 和 Poisson 检验在多种备择假设下的有效性。该检验工具箱被应用于分析北极熊的哺乳模式。
英文摘要
We develop a unified framework for $c$-sample homogeneity testing on the circle. The proposed class of $c$-sample Sobolev tests generalizes the two-sample Sobolev tests based on uniform scores and encompasses the existing multisample tests as particular cases. We further embed this class into a broader aggregation framework, where the samplewise Sobolev components are combined through general merging functions, including average-type, maximum-type, and interpolating families. Within this class, we introduce the first Anderson-Darling-type homogeneity test for circular data, and we further propose two new tests designed to detect multimodal departures from homogeneity, constructed from softmax and Poisson kernels. We derive the asymptotic null distribution of the class, prove its consistency against a broad family of fixed alternatives, and obtain the asymptotic distribution under shift-type local alternatives. The tests are distribution-free and therefore do not require resampling. A comprehensive simulation study demonstrates the strong power of the Anderson-Darling-type test compared with Cramér-von Mises-type competitors across several scenarios, and the effectiveness of the softmax and Poisson tests under several alternatives. The testing toolbox is applied to analyze the nursing patterns of polar bears.
Comments24 pages, 6 figures, 4 tables. Supplementary material: 30 pages, 1 figure, 1 table
