一种自动有限样本稳健性度量：何时删除少量数据会产生重大影响？
An Automatic Finite-Sample Robustness Metric: When Can Dropping a Little Data Make a Big Difference?
AI总结：
针对研究样本与目标总体非随机偏离可能导致结论对少量数据过度敏感的问题，提出基于经典影响函数的近似最大影响扰动度量，可自动计算常用计量方法的有限样本稳健性，发现部分经济学论文结论移除不到1%样本即可被推翻。
摘要：
研究样本通常会以非随机的方式与推断和政策决策的目标总体存在差异。研究人员通常认为，这类由总体随时间和空间的变化，或真正随机抽样的困难导致的偏离随机抽样的情况是微小的，其对推断的相应影响也应该很小。因此，如果我们的研究结论对样本中极小比例的数据过度敏感，我们可能会对此感到担忧。\n我们提出了一种方法，用于评估应用计量经济学结论对移除小部分样本的敏感性。手动检查所有可能的小子集的影响在计算上是不可行的，因此我们使用一种近似方法来寻找最具影响力的子集。我们的度量指标“近似最大影响扰动（Approximate Maximum Influence Perturbation）”基于经典影响函数，可针对包括（但不限于）OLS、IV、MLE、GMM和变分贝叶斯在内的常用方法自动计算。\n我们给出了近似性能的有限样本误差界，并以极低的额外成本提供了敏感性的精确有限样本下界。我们发现，敏感性由推断问题中的信噪比驱动，无法通过标准误差反映，不会渐近消失，也并非由模型误设导致。虽然部分实证应用具备稳健性，但数篇有影响力的经济学论文的结论可通过移除不到1%的样本被推翻。
英文摘要：
Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or difficulties in sampling truly randomly -- are small, and their corresponding impact on the inference should be small as well. We might therefore be concerned if the conclusions of our studies are excessively sensitive to a very small proportion of our sample data. We propose a method to assess the sensitivity of applied econometric conclusions to the removal of a small fraction of the sample. Manually checking the influence of all possible small subsets is computationally infeasible, so we use an approximation to find the most influential subset. Our metric, the "Approximate Maximum Influence Perturbation," is based on the classical influence function, and is automatically computable for common methods including (but not limited to) OLS, IV, MLE, GMM, and variational Bayes. We provide finite-sample error bounds on approximation performance. At minimal extra cost, we provide an exact finite-sample lower bound on sensitivity. We find that sensitivity is driven by a signal-to-noise ratio in the inference problem, is not reflected in standard errors, does not disappear asymptotically, and is not due to misspecification. While some empirical applications are robust, results of several influential economics papers can be overturned by removing less than 1% of the sample.
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