发表机构
Universidad de Sevilla; Instituto de Matemáticas de la Universidad de Sevilla（塞维利亚大学; 塞维利亚大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对通过U统计量定义的参数在多独立总体中的相等性检验，提出通用框架，考虑Wald型和ANOVA型统计量，推导其渐近分布，构建无参数假设的检验程序，研究替代零分布估计器，经模拟研究和实际应用验证了方法的有效性。
AI 中文摘要
本文提出了一个通用且统一的框架，用于检验通过U统计量定义的广泛参数类在多个独立总体中的相等性。该方法涵盖各种常见统计问题，如比较方差、相关系数或基尼指数等。考虑了两个检验统计量，一个是Wald型统计量，另一个是ANOVA型统计量。推导了第一个统计量在固定维度下的渐近分布，研究了第二个统计量在固定维度和维度增加（参数维度随样本量发散）下的情况。基于这些极限分布构建了无需参数假设的渐近精确推断检验程序。还研究了基于加权自举近似的替代零分布估计器，适用于固定维度下的ANOVA型统计量。通过广泛的模拟研究评估了所提程序的有限样本性能和计算效率。最后，对一个真实数据集的应用说明了所提方法的有用性。
英文摘要
This paper proposes a general and unified framework for testing the equality of a broad class of parameters, defined as a smooth function of expectations of symmetric kernels, across multiple independent populations. We consider two test statistics, a Wald-type statistic and an ANOVA-type statistic. The asymptotic distribution of the first one is derived under a fixed-dimension regime, whereas the second one is studied under both fixed and increasing-dimension regimes, where the parameter dimension diverges with the sample size. Based on these limiting distributions, we construct test procedures enabling asymptotically exact inference without parametric assumptions. Additionally, an alternative null distribution estimator based on a weighted bootstrap approximation is studied, which is applicable to the ANOVA-type statistic under a fixed-dimension regime. The finite-sample performance and computational efficiency of the proposed procedures are evaluated through an extensive simulation study and a real dataset application.
