We present a sequential version of the kernelized Stein discrepancy, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the sample size need not be fixed prior to data collection; the practitioner can choose whether to stop the test or continue to gather evidence at any time while controlling the false discovery rate. In stark contrast to related literature, we do not impose uniform boundedness on the Stein kernel. Instead, we exploit the potential boundedness of the Stein kernel at arbitrary point evaluations to define test martingales, that give way to the subsequent novel sequential tests. We prove the validity of the test, as well as an asymptotic lower bound for the logarithmic growth of the wealth process under the alternative. We further illustrate the empirical performance of the test with a variety of distributions, including restricted Boltzmann machines.

本文解决了对未规范密度进行适应性停止的适合度检验问题，提出了一种顺序版本的核化斯坦差异。该方法在不需固定样本量的情况下，允许研究者在检验过程中自主选择停止或继续采集数据，进而控制假发现率。研究结果证实了检验的有效性，并展示了其对多种分布的实证表现。

顺序核化斯坦差异