【专家简介】：郭旭，现任北京师范大学统计学院教授，博士生导师。曾荣获北京师范大学第十一届“最受本科生欢迎的十佳教师”，北京师范大学第十八届“青教赛”一等奖和北京市第十三届“青教赛”三等奖。目前主要关注高维回归模型中的假设检验问题也对基于机器学习算法的统计推断感兴趣，有多篇文章发表在统计学和计量经济学国际顶尖期刊包括JRSSB, JASA, Biometrika, JOE和JMLR，担任统计学国际知名期刊JMVA副主编。
【报告摘要】：We propose a new procedure MATCH (Multiplier-Assisted Tests for Conditional Hypotheses) to test whether the non-Euclidean data match the target model, which is a general framework for significance and specification testing in Fréchet regression. MATCH covers global significance, partial significance, and the adequacy of global Fréchet regression, providing a unified way to compare unrestricted conditional Fréchet means with restricted alternatives. One of the key challenges is that the ordinary held-out loss difference is first-order degenerate under the null: the oracle losses coincide, and plug-in statistics is dominated by nuisance estimation error. MATCH uses sample splitting and independent random multipliers on held-out losses to create a nondegenerate Gaussian leading term without residuals or tangent-space coordinates. To improve data use and stability, we further develop cross-fitted tests and repeated cross-fitting with p-value merging. We establish asymptotic null validity, consistency under fixed alternatives, and local power guarantees. Simulations for distributional, symmetric positive-definite (SPD) matrix-valued, and spherical responses support the theoretical findings, and applications to county-level household income distributions and North Atlantic tropical-cyclone locations demonstrate the practical use of the proposed tests.
【报告时间】：2026年09月21日（周一）16:40-17:40
【报告地点】：位育楼417
