度量空间上分布的拟合优度检验
Goodness-of-fit for distributions on metric spaces
浏览论文内容
中文总结 AI 辅助
针对度量空间上的分布，提出基于距离轮廓的拟合优度检验框架，涵盖复合原假设、渐近性质及自助法，并在球面等数据上验证有效性。
中文摘要 AI 辅助
我们提出了一个在可分度量空间上分布的通用拟合优度检验框架。在适当的可识别性条件下，概率分布由距离轮廓（distance profiles）刻画，这促使我们将其用于简单和复合原假设下的拟合优度检验。对于复合原假设，参数估计通过Bahadur型展开纳入，并在原假设下获得了距离轮廓经验过程的渐近分布。我们基于该经验过程定义检验统计量，并推导其渐近零分布。我们进一步研究了所提检验在固定备择和局部备择下的行为，建立了相合性结果。开发了乘子自助法（multiplier bootstrap）程序，并在简单和复合原假设下建立了其条件渐近有效性。该方法通过模拟研究和在球面、双曲面和单纯形上的实际数据应用进行了说明。
英文摘要
We propose a general goodness-of-fit framework for distributions on separable metric spaces. Under suitable identifiability conditions, probability distributions are characterized by distance profiles, which motivates their use in goodness-of-fit testing, for simple and composite null hypotheses. For composite null hypotheses, parameter estimation is incorporated via a Bahadur-type expansion, and the asymptotic distribution of the empirical process for distance profiles is obtained under the null. We define test statistics based on this empirical process and derive their asymptotic null distributions. We further study the behavior of the proposed tests under fixed and local alternatives, establishing consistency results. Multiplier bootstrap procedures are developed, and their conditional asymptotic validity is established under both simple and composite null hypotheses. The methodology is illustrated with simulation studies and real-data applications for data on the sphere, hyperboloid, and simplex.
发表机构
- Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
- KU Leuven（鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。
