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摘要翻译：
当比较两个分布时，了解在哪个分位数或值有统计上的显著差异通常是有帮助的。这比全局拟合优度测试的二进制“拒绝”或“不拒绝”决定提供了更多的信息。我们将我们的问题描述为跨越分位数$\tau\in(0,1)$或值$R\in\mathbb{R}$连续体的多重测试，我们证明了Kolmogorov-Smirnov测试（解释为多重测试过程）实现了对家族错误率的强控制。然而，其尾翼灵敏度低的众所周知的缺陷仍然存在。我们提供了一种替代方法，它保留了对家族错误率的如此强的控制，同时也具有均匀的灵敏度，即在分布的每个$n\\\infty$阶统计量上，点态I型错误率相等。我们的单样本方法立即计算，使用我们的新公式，也立即计算拟合优度$P$-值和一致的置信度带。为了提高功率，我们还提出了步进和预测试程序，以保持对渐近家族错误率的控制。考虑了单样本和两样本情况，以及回归间断设计和条件分布的推广。提供了模拟、经验示例和代码。
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英文标题：
《Comparing distributions by multiple testing across quantiles or CDF
values》
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作者：
Matt Goldman, David M. Kaplan
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最新提交年份：
2017
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global goodness-of-fit test. Framing our question as multiple testing across the continuum of quantiles $\tau\in(0,1)$ or values $r\in\mathbb{R}$, we show that the Kolmogorov--Smirnov test (interpreted as a multiple testing procedure) achieves strong control of the familywise error rate. However, its well-known flaw of low sensitivity in the tails remains. We provide an alternative method that retains such strong control of familywise error rate while also having even sensitivity, i.e., equal pointwise type I error rates at each of $n\to\infty$ order statistics across the distribution. Our one-sample method computes instantly, using our new formula that also instantly computes goodness-of-fit $p$-values and uniform confidence bands. To improve power, we also propose stepdown and pre-test procedures that maintain control of the asymptotic familywise error rate. One-sample and two-sample cases are considered, as well as extensions to regression discontinuity designs and conditional distributions. Simulations, empirical examples, and code are provided.
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PDF链接：
https://arxiv.org/pdf/1708.04658
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