发表机构
School of Statistics, Renmin University of China; Yau Mathematical Science Center, Tshinghua University（中国人民大学统计学院; 清华大学丘成桐数学科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
SPARK提出一种基于残差投影的通用拟合优度检验框架，适用于传统模型与黑盒学习器、连续与二元响应及低高维预测变量，通过去偏和核投影方法提取剩余信号，并验证其渐近性质与有效性。
AI 中文摘要
拟合优度检验是评估拟合过程是否捕获了协变量中包含的系统信息的基本工具。传统理论主要关注参数回归模型，而现代数据分析越来越依赖于灵活的黑盒学习器，仅凭其预测成功不足以评估模型准确性。在本文中，我们提出SPARK，一个通用的拟合优度检验框架，适用于传统统计模型和一般黑盒学习过程、连续和二元响应，以及低维和高维预测变量。基于去偏策略，将学习过程初始拟合的残差投影到近乎正交的方向上以提取任何剩余信号。为了捕获所有投影方向上的信息，我们提出了一种基于核的投影方法，并建立了其渐近性质和自助法过程的一致性。综合模拟和真实数据分析证明了我们提出方法的有效性和灵活性。
英文摘要
Goodness-of-fit testing is a basic tool for assessing whether a fitted procedure has captured the systematic information contained in the covariates. While traditional theory has largely focused on parametric regression models, modern data analysis increasingly relies on flexible black-box learners, whose predictive success alone is insufficient to assess model accuracy. In this paper, we propose SPARK, a general framework for goodness-of-fit testing that applies to traditional statistical models and general black-box learning procedures, continuous and binary responses, and low- and high-dimensional predictors. Based on a debiasing strategy, the residuals from an initial fit of a learning procedure are projected onto nearly orthogonal directions to extract any remaining signal. To capture information across all projection directions, we propose a kernel-based projection method and establish both its asymptotic properties and the consistency of a bootstrap procedure. Comprehensive simulations and real data analyses illustrate the effectiveness and flexibility of our proposed method.
Comments50 pages, 11 figures
