数据重用与误差的长久阴影：分割、抽样与前瞻性管理推断误差
Data Reuse and the Long Shadow of Error: Splitting, Subsampling, and Prospectively Managing Inferential Errors
AI总结：
本文研究了数据重用对测试过程依赖性的影响，提出通过个体研究者层面的抽样技术减少依赖，建立渐近联合正态性理论，并利用均值-方差投资理论定义预期方差比，证明数据分割在确保独立性时是渐近最优的。
摘要：
当多个研究者分析共同数据集时，数据重用会引发测试过程间的依赖，影响误差分布。现有管理依赖测试的方法需要跨研究协调或事后修正，但无法适用于当前独立研究者在共享数据集上评估假设的实践。本文研究了在个体研究者层面实施的抽样技术以减少依赖，最小化协调。为此，我们建立了渐近联合正态性理论，将协方差矩阵分解为数据重叠项和测试统计量关联项。这种分解表明，控制数据重叠足以控制依赖，我们通过预期方差比的概念进行形式化。这使得可以在全局空假设下，以测试统计量的配对相关性为函数，推导联合拒绝域的方差。我们采用均值-方差投资理论来衡量风险，定义预期方差比（EVR）为类型I错误计数的预期方差与独立基线的比率。我们证明数据分割在确保独立性的规则中是渐近最优的。然后利用集中不等式证明个体研究者可实施的抽样技术可以确保EVR接近1。最后，我们证明此类抽样技术能够同时执行多个测试并确保足够的功效，并且受限制的EVR与数据分割相比为O(1/r²)，其中r是每个统计量所需数据的比例。
英文摘要：
When multiple investigators analyze a common dataset, the data reuse induces dependence across testing procedures, affecting the distribution of errors. Existing techniques of managing dependent tests require either cross-study coordination or post-hoc correction. These methods do not apply to the current practice of uncoordinated groups of researchers independently evaluating hypotheses on a shared dataset. We investigate the use of subsampling techniques implemented at the level of individual investigators to remedy dependence with minimal coordination. To this end, we establish the asymptotic joint normality of test statistics for the class of asymptotically linear test statistics, decomposing the covariance matrix as the product of a data overlap term and a test statistic association term. This decomposition shows that controlling data overlap is sufficient to control dependence, which we formalize through the notion of Expected Variance Ratio. This enables the closed form derivation of the variance of the joint rejection region under the global null as a function of pairwise correlations of test statistics. We adopt mean-variance portfolio theory to measure risk, defining the Expected Variance Ratio (EVR) as the ratio of the expected variance of the Type I error count to the independent baseline. We show that data splitting is asymptotically optimal among rules that ensure exact independence. We then use concentration inequalities to establish that subsampling techniques implementable by individual investigators can ensure an EVR close to $1$. Finally, we show that such subsampling techniques are able to simultaneously perform a number of tests while ensuring sufficient power and that the bounded EVR is $O\left(\frac{1}{r^2}\right)$ compared to data splitting's $O\left(\frac{1}{r}\right)$, where $r$ is the per-statistic fraction of data required.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
