论文标题
功能数据的内核两样本测试
A Kernel Two-Sample Test for Functional Data
论文作者
论文摘要
我们提出了一种基于最大平均差异（MMD）的非参数两样本测试程序，用于测试使用在功能空间上定义的内核，即两个函数样本具有相同的基础分布的假设。这种构建是由对增加维度数据集的基于MMD测试的效率进行扩展分析的动机。内核在功能空间及其相关MMD上的理论特性被建立并用于确定新提出的测试的功效，并评估基于离散功能样本的功能重建的效果。理论结果在一系列合成和现实世界数据集中得到了证明。
We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This construction is motivated by a scaling analysis of the efficiency of MMD-based tests for datasets of increasing dimension. Theoretical properties of kernels on function spaces and their associated MMD are established and employed to ascertain the efficacy of the newly proposed test, as well as to assess the effects of using functional reconstructions based on discretised function samples. The theoretical results are demonstrated over a range of synthetic and real world datasets.
