用核方法检验分布是否等价，解决传统方法无法确认无差异的缺陷。
Kernel Tests of Equivalence
- 基于核Stein散度和最大均值差异设计等价检验方法
- 在设定差异阈值下通过渐近正态或自助法确定临界值
- 适用于非参数分布全量比较，适合需要确认无差异的研究
我们提出新的基于核的方法来检验分布之间的等价性。传统拟合优度检验无法可靠判断分布差异的缺失，因为零假设不被拒绝可能只是检验力不足（第二类错误）。这促使了等价检验的发展，旨在在控制误差率下评估统计上无意义的效应是否存在。然而，现有等价检验要么局限于参数分布，要么仅关注特定矩而非整个分布。本文利用两种基于核的统计差异度量——核Stein散度和最大均值差异，克服这些局限。所提检验的零假设为候选分布与名义分布的差异至少达到预设阈值，该阈值由上述度量衡量。我们提出了两种计算检验临界值的方法：一种基于渐近正态近似，另一种基于自助抽样。通过数值实验评估了这些测试的性能。
原文摘要 · Abstract (English)
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null hypothesis may simply be a result of lack of test power, also known as the Type-II error. This motivates \emph{equivalence testing}, which aims to assess the \emph{absence} of a statistically meaningful effect under controlled error rates. However, existing equivalence tests are either limited to parametric distributions or focus only on specific moments rather than the full distribution. We address these limitations using two kernel-based statistical discrepancies: the \emph{kernel Stein discrepancy} and the \emph{Maximum Mean Discrepancy}. The null hypothesis of our proposed tests assumes the candidate distribution differs from the nominal distribution by at least a pre-defined margin, which is measured by these discrepancies. We propose two approaches for computing the critical values of the tests, one using an asymptotic normality approximation, and another based on bootstrapping. Numerical experiments are conducted to assess the performance of these tests.
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