统计与数据科学系系列学术报告之四百九十期

时间： 2025年10月30日（周四）10:00-11:00

主持人：复旦大学管理学院统计与数据科学系黎德元教授

地点：史带楼410室

报告人：张正军教授

中国科学院大学

题目：Indirect Statistical Inference with Guaranteed Necessity and Sufficiency

摘要：This talk will introduce a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an assumed distribution with those from simulated unit exponential samples, the ranked quotients exhibit distinct asymptotics: the left segment converges to a non-degenerate distribution, while the middle and right segments degenerate to one. This yields a necessary and sufficient condition in probability for two sequences of continuous random variables to follow the same distribution. Building on this, we propose an optimization criterion based on relative errors between ordered samples. The criterion achieves its minimum if and only if the assumed and true distributions coincide, providing a second necessary and sufficient condition in optimization. These dual NS properties, rare in the literature, establish a fundamentally stronger inference framework than existing methods. Unlike classical approaches based on absolute errors (e.g., Kolmogorov–Smirnov), NSE exploits relative errors to ensure faster convergence, requires only mild approximability of the cumulative distribution function, and provides both point and interval estimates. Simulations and real-data applications confirm NSE’s superior performance in preserving distributional assumptions where traditional methods fail. Our work shows that some pillars of modern statistics are no longer indispensable once a necessary-and-sufficient estimation framework becomes available. Joint work with Xinyang Hu, Chuyang Lu, and Tianyin Liu.

个人简介：张正军，中国科学院大学经济与管理学院长聘教授和统计与数据科学系系主任，中国科学院预测科学研究中心副主任，原美国威斯康辛大学统计系终身教授和系副主任，威斯康辛大学生物医学信息系兼职教授，国际数理统计协会执行委员和财务总监（July 2016 -- July 2022），国际数理统计协会会士，美国统计协会会士。现担任JASA，JBES， Statistica Sinica， JDS， EJS、STaRF等国际期刊副主编。主要研究方向包括统计理论和方法、计量经济学、金融计量学、计算医学与实践、极端气候等等。在国际顶级期刊：统计（AoS，JASA，JRSSB）、计量（JoE, EE）、金融（JBES, JBF）、医学（AFM，Vaccines，npj Precision Oncology）、气象 (ATM) 等发表论文上百篇。代表性工作和首创性思想和作品包括: 新极值理论、绝对和相对同步有效性（AbRelaTEs）、双边截断极值惩罚变量选择机器学习模型（TWT-LR-ETP）、商相关系数（QCC、TQCC）、非对称广义相关系数（GMC）、滞后尾部相依系数(lambda_k)、最大线性回归模型(MaxLR)、最大逻辑回归模型(Max-logistic)、EGB2期权定价公式、盯市在险价值（MMVaR）、条件极值Frechet自回归（AcF）, 虚拟标准数字货币（VSTC），新冠基因组学、癌症基因组学的几何空间（DARPA： Mathematical Challenge Fifteen: The Geometry of Genome Space）等等。