AI 中文总结
研究提出用顺序校准的二级统计量增强拟合优度检验的方法，通过条件校准实现总体第一类错误的乘法分解及初级阶段水平调整，以有序拒绝区域分解功效，模拟显示该方法能提升对多种备择假设的检验功效。
AI 中文摘要
拟合优度统计量对不同类型的备择假设可能具有显著不同的功效。我们提出了一种顺序程序，用有序的二级统计量集合增强主要的拟合优度统计量。在每个阶段，当前统计量的接受区域在零分布下根据所有先前阶段的接受情况进行校准。这种条件校准给出了总体第一类错误的简单乘法分解，并允许在选择二级阶段水平后明确调整初级阶段水平。不相交的逐阶段拒绝区域也提供了功效的有序首次拒绝分解。我们通过用样本方差和样本偏度增强柯尔莫哥洛夫 - 斯米尔诺夫统计量来说明该方法。在标准正态零假设下的模拟中，所得的链式程序在保留几乎所有主要检验对位置备择假设的功效的同时，显著提高了对尺度、重尾和非对称备择假设的功效。颠倒二级统计量的顺序在实验中产生几乎相同的总功效，尽管功效的逐阶段归因可能会有很大变化。
英文摘要
An omnibus goodness-of-fit statistic can fail to exploit simple diagnostic evidence efficiently. For example, under a standard normal null, an exceptionally large observation is direct evidence of a scale or tail departure even when the primary omnibus statistic does not cross its critical value. This motivates a simple augmentation principle: retain an established primary test, but reserve a small part of its null rejection budget for secondary statistics that encode natural features such as variation, asymmetry, or tail behavior. We implement this principle by calibrating each secondary acceptance region under the null conditional on acceptance at all preceding stages. Once calibrated, the resulting test is a fixed rectangular acceptance rule; the ordering is a mechanism for choosing its boundaries and assigning ordered first-rejection contributions, not a sequential-sampling scheme. An unconditional stage-budget parameterization makes the central trade-off explicit: additional sensitivity is purchased by removing a prespecified, usually small, amount of rejection probability from the primary stage. We establish strong consistency of the quantile-based Monte Carlo calibration and give an observation-specific pooled-rank version with exact randomized finite-m null size. In an experiment under a standard normal null with n=10, we augment the Kolmogorov--Smirnov statistic with sample variance and sample skewness. Assigning only 0.75% of the total Type I error budget to the two secondary statistics changes power against N(0.5,1) from 0.2742 to 0.2733, while increasing power against N(0,0.2^2) from 0.4693 to 0.9827. This focused experiment is a proof of principle rather than an exhaustive comparison of normality tests: a small unconditional allocation to prespecified diagnostics can greatly broaden power while preserving almost all of the primary test's power.
CommentsAdded several propositions to support empirical claims. Broadened the experiment with sensitivity analysis. Restructured the text for clarity
