报告题目： Indirect Statistical Inference with Guaranteed Necessity and Sufficiency

报 告 人：张正军（中国科学院大学教授）

报告时间：2025年11月21日（星期五下午）15：30-17：00

报告地点： 格物楼528报告厅

报告摘要：This talk will introduece 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.

报告人简介：张正军，教授，中国科学院大学统计与数据科学系主任，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教授和系副主任。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) 等发表论文百余篇。