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在线学术报告 | 张正军教授:通往精准统计推断之路所需的必要充分估计

狗熊会 狗熊会 2023-10-08


  

  


摘要

The existing statistical estimations were often derived from some sufficient conditions but not necessary. We first establish a fundamental theorem that guarantees the transformed order statistics from the assumed distribution of a random variable (or an error term) to be arbitrarily close to the order statistics of a simulated sequence of the same distribution. The theorem leads to a necessary and sufficient condition for two series of random variables to follow the same distribution. Based on the condition, we propose a new necessary and sufficient estimation (NSE) method for preserving continuous distribution assumptions in various statistical studies. Unlike the Kolmogorov-Smirnov statistics and many other statistics based on absolute errors between the empirical distribution and the assumed distribution, the statistics proposed are based on relative errors between the transformed and simulated order statistics. Surprisingly, relative errors result in much faster convergence rates than absolute errors. Using the constructed statistic (or the pivotal quantity in estimation) to measure the relative distance between two ordered samples, we estimate parameters to minimize the distance. Furthermore, unlike many existing methods, which rely on some regularity conditions and/or the explicit forms of probability density functions, the NSE only assumes a mild condition that the cumulative distribution function can be approximated to a satisfying precision. The NSE can be directly applied to many kinds of statistical distribution inference problems regardless of whether existing estimation methods are applicable. Furthermore, the NSE provides not only point estimations but also interval estimations to first preserve the model assumption and then guarantee the significance of parameters. Using NSE, researchers and practitioners no longer need to assume any moment conditions to derive asymptotic results. There is no need to conduct the bootstrap method when the limiting distributions are not computable. This talk illustrates simulation examples and real applications to show NSE's superior performance for various commonly applied inference problems where existing estimation methods may fail to guarantee desired distributional assumptions. Joint work with Bingyan Wang (Princeton) and Xinyang Hu (Yale).

嘉宾介绍

张正军教授现为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,原美国威斯康辛大学统计系终身教授和系副主任,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)、气象 (ATM) 等发表论文上百篇。代表性和创新性思想和作品包括商相关系数(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。


狗熊会线上学术报告厅向数据科学及相关领域的学者及从业者开放,非常期待各位熊粉报名或推荐报告人。相关事宜,请联系:常莹,ying.chang@clubear.org

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