使用最近邻图的条件均值独立性与全局敏感性分析
Conditional Mean Independence, Global Sensitivity Analysis, and Variable Screening Using nearest neighbor Graphs
- Boston University（波士顿大学）
- University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究如何用条件均值函数解释响应，基于最近邻图提出该测度的一致估计量，给出收敛速度，用于条件均值独立性检验及无模型变量筛选，还讨论了交互效应测量的扩展。
AI中文摘要：
量化条件均值函数对响应的解释程度对许多统计任务至关重要。本文提出基于最近邻图的该测度的一致估计量，推导其收敛速度，给出条件均值独立性检验方法，还用于无模型变量筛选，讨论了交互效应测量扩展，通过模拟和实例展示了方法优势。
英文摘要：
Quantifying how much of the variation in a response is explained by its conditional mean is central to many statistical problems. In this paper, we develop a unified framework for this problem, centered on a normalized conditional mean discrepancy that coincides with the classical Sobol' index for univariate responses and its natural trace-based extension for multivariate responses. We propose a simple estimator of this measure based on nearest-neighbor graphs that can be computed in near-linear time. We establish its consistency and derive its rate of convergence. Further, under the null hypothesis of conditional mean independence, a studentized version of the statistic is asymptotically standard normal. This leads to a computationally efficient test for conditional mean independence that attains the correct asymptotic level and is universally consistent, without requiring bootstrap calibration or sample splitting. Building on the same estimator, we develop a model-free sequential variable-screening procedure that selects a sufficient set with high probability and an exponential error bound. We also discuss extensions of the framework to quantifying interaction effects through higher-order Sobol' indices. Simulations and real-data experiments demonstrate strong power, effective variable screening, and substantial computational gains over existing methods.
