Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified through influential diagnostics, which aim to capture observations that unduly bias model estimation. To date, methods for identifying observations that influence the selection of a stochastically chosen submodel have been underdeveloped, especially in the high-dimensional setting where the number of predictors $p$ exceeds the sample size $n$. Recently we proposed an improved diagnostic measure to handle this setting. However, its distributional properties and approximations have not yet been explored. To address this shortcoming, we revisit the notion of exchangeability to determine the exact asymptotic distribution of our assessment measure. This foundation enables the introduction of theoretically supported parametric and nonparametric approaches for distributional approximation and derivation of thresholds for outlier identification. The resulting framework is further extended to logistic regression models and evaluated by comprehensive simulation studies comparing the performance of various detection methods. Finally, the framework is applied to data from a task-based fMRI study of thermal pain, with the goal of identifying outliers that distort the formulation of the statistical model using functional brain activity to predict physical pain ratings. Both linear and logistic models are used to demonstrate the benefits of detection and compare the performance of different detection procedures. In particular, we identify two influential observations that were not detected in prior studies

翻译：异常观测值在广泛的科学领域中频繁出现，对统计模型的普适性及下游分析的可重复性构成显著挑战。这些观测值通过影响诊断方法进行识别，其目的在于捕捉那些对模型估计产生不当偏差的观测值。迄今为止，针对影响随机选择子模型筛选的观测值的识别方法尚不完善，尤其是在预测变量数量$p$超过样本量$n$的高维场景中。近期我们提出了一种改进的诊断度量来处理此场景。然而，其分布特性与近似方法尚未得到探究。为弥补此不足，我们重新审视可交换性概念，以确定我们评估度量的精确渐近分布。此基础使得引入理论支持的参数化与非参数化方法成为可能，用于分布近似及推导异常值识别阈值。所得框架进一步扩展至逻辑回归模型，并通过综合模拟研究评估各种检测方法的性能。最后，该框架应用于一项基于任务的功能磁共振成像热痛研究数据，旨在识别那些扭曲统计模型构建的异常值——该模型利用功能性大脑活动预测物理疼痛评分。研究同时采用线性模型与逻辑回归模型来展示检测的益处，并比较不同检测流程的性能。特别地，我们识别出两个在先验研究中未被发现的影响观测值。