标题： 高维回归中的自适应影响诊断 显示英文标题

标题： Adaptive Influence Diagnostics in High-Dimensional Regression

摘要： 一种自适应Cook距离（ACD）用于在高维单指标模型中诊断具有多重共线性和异常值污染的显著观测点。ACD是一种基于稀疏局部线性梯度的无模型技术，以减弱杠杆效应。在包含强相关性的低维和高维设计设置的模拟中，基于LASSO（ACD-LASSO）和SCAD（ACD-SCAD）惩罚的ACD相对于经典Cook距离和局部影响以及LASSO的DF-Model和Case-Weight调整解决方案减少了掩盖和淹没现象。由ACD标记的修剪点稳定了变量选择同时保留了核心信号。应用于两个数据集——1960年美国城市污染研究和一个高维核黄素基因组实验，显示出选择稳定性和可解释性的持续提升。 显示英文摘要

摘要： An adaptive Cook's distance (ACD) for diagnosing influential observations in high-dimensional single-index models with multicollinearity and outlier contamination is proposed. ACD is a model-free technique built on sparse local linear gradients to temper leverage effects. In simulations spanning low- and high-dimensional design settings with strong correlation, ACD based on LASSO (ACD-LASSO) and SCAD (ACD-SCAD) penalties reduced masking and swamping relative to classical Cook's distance and local influence as well as the DF-Model and Case-Weight adjusted solution for LASSO. Trimming points flagged by ACD stabilizes variable selection while preserving core signals. Applications to two datasets--the 1960 US cities pollution study and a high-dimensional riboflavin genomics experiment show consistent gains in selection stability and interpretability.