AI 中文总结
本文提出一种基于归一化流的分解方法，在干扰参数存在时自动发现近似枢轴统计量，具有良好检验功效，优于Welch检验和轮廓似然比方法。
AI 中文摘要
我们提出了一种基于神经网络的归一化流的简单分解方法，该方法仅基于感兴趣分布的样本生成器，在存在干扰参数的情况下自然揭示出一个枢轴统计量（或近似枢轴统计量）。我们证明该统计量在最小平均KL散度意义下近似枢轴，即其p值分布接近均匀分布，并论证当统计量维度等于参数维度时，该统计量可预期具有良好的检验功效。该方法能够整合关于平移和缩放等群不变性的先验知识。它几乎能精确地发现单样本t检验，在受限方差比范围内，其最坏情况下的检验尺度优于Welch检验，并在偏双列相关系数上实现良好的校准，同时在中小样本上比轮廓似然比技术具有更高的检验功效（且速度更快）。
英文摘要
We present a simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic (or something close) in the presence of nuisance parameters, based only on a sample generator from the distribution of interest. We show that the statistic is near-pivotal in the sense of minimum average KL-divergence of its $p$-values versus uniform and we argue that it can be expected to have good power when the dimension of the statistic equals the dimension of the parameter. It is able to incorporate prior knowledge about group invariances such as translation and scale. It can discover the one-sample $t$-test almost exactly, outperforms the Welch test in terms of worst-case size over a constrained variance-ratio range and achieves good calibration on partial biserial correlations, while showing higher power (and being much faster) on small-to-moderate samples than profile likelihood-ratio techniques.
Comments49 pages and 13 figures, including appendices. Code available at https://github.com/philassheton/NeuralCIs
