发表机构
School of Statistics, East China Normal University; School of Management, University of Science and Technology of China（华东师范大学统计学院; 中国科学技术大学管理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对随机对象响应的回归问题，提出边际坐标检验方法，结合半监督设计与KCMD统计量，建立相关理论性质并通过模拟和出租车流量分析验证，实现了条件均值依赖的有效检验。
AI 中文摘要
我们针对具有欧几里得预测变量和可分度量空间中随机对象响应的回归问题，提出了一种边际坐标检验方法。该方法旨在检验在给定其余预测变量的条件下，某一预测变量是否提供了关于响应的额外信息。在半监督设计中，利用未标记样本估计预测变量的条件均值，同时保留独立的标记样本用于推断。所得残差与乘积空间核结合，形成无需响应残差的核条件均值依赖（KCMD）U统计量。基于恒等式的主检验针对必要的条件均值限制，而多变换扩展则探测更广泛的备择假设。我们建立了加权中心卡方原假设极限、wild bootstrap的有效性、对固定可检测备择的一致性，以及均值元素备择下的局部功效。对于同时推断，截断p-to-e校准结合e-BH方法，在一般依赖下提供渐近错误发现率控制。针对欧几里得和非欧几里得响应的模拟，以及纽约市出租车流量分析，验证了该方法的有效性。
英文摘要
We develop a marginal coordinate test for regression with Euclidean predictors and a random-object response in a separable metric space. The goal is to test whether a predictor provides additional information about the response conditional on the remaining predictors. In a semi-supervised design, an unlabeled sample is used to estimate predictor conditional means, while an independent labeled sample is reserved for inference. The resulting residuals are combined with a product-space kernel to form a kernel conditional mean dependence (KCMD) U-statistic without requiring a response residual. The primary identity-based test targets a necessary conditional mean restriction, while a multiple-transformation extension probes broader alternatives. We establish a weighted centered chi-square null limit, wild bootstrap validity, consistency against fixed detectable alternatives, and local power under mean-element alternatives. For simultaneous inference, truncated p-to-e calibration combined with e-BH provides asymptotic false discovery rate control under general dependence. Simulations with Euclidean and non-Euclidean responses, together with a New York City taxi-flow analysis, illustrate the method.
Comments34 pages, 4 tables
