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2019概率统计及其应用系列报告之七(张正军)

  发布日期:2019-05-22  浏览量:452


: Simulated Distribution Based Learning for Non-regular and Regular Statistical Inferences

报 告 人: 张正军(美国威斯康星大学麦迪逊分校教授,Journal of Business & Economic StatisticsStatistica Sinica副主编)

要:Statistical research involves drawing inference about unknown quantities (e.g., parameters) in the presence of randomness in which distribution assumptions of random variables (e.g., error terms in regression analysis) play a central role. However, a fundamental issue of preserving the distribution assumptions has been more or less ignored by many inference methods and applications. As a result, the further inference of studied problems and related decisions based on the estimated parameter values may be inferior. This paper proposes a continuous distribution preserving estimation approach for various kinds of non-regular and regular statistical studies. The paper establishes a fundamental theorem which guarantees the transformed order statistics (to a given marginal) 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 marginal distribution. Different from the Kolmogorov-Smirnov test which is based on absolute errors between the empirical distribution and the assumed distribution, the statistics proposed in the paper are based on relative errors of the transformed order statistics to the simulated ones. Upon using the constructed statistic (or the pivotal quantity in estimation) as a measure of the relative distance between two ordered samples, we estimate parameters such that the distance is minimized. Unlike many existing methods, e.g., maximum likelihood estimation, which rely on some regularity conditions and/or the explicit form of probability density function, the new method only assumes a mild condition that the cumulative distribution function can be approximated to a satisfied precision. The paper illustrates simulation examples to show its superior performance. Under the linear regression settings, the proposed estimation performs exceptionally well regarding preserving the error terms (i.e., the residuals) to be normally distributed which is a fundamental assumption in the linear regression theory and applications.

报告时间: 2019529()  10:00-11:00

报告地点:磬苑校区澳门赌搏网站大全H306

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数学科学学院

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专家概况:

张正军教授现为美国威斯康星大学麦迪逊分校统计系长聘正教授、美国统计协会会士、国际数理统计协会财务总监、国际顶级期刊Journal of Business & Economic Statistics副主编、Statistica Sinica副主编、Journal of Econometrics金融工程与风险管理特刊共同主编;北卡罗来纳大学教堂山分校统计学博士,北京航空航天大学管理工程博士。主要研究方向包括:金融时间序列分析、极值理论、异常气候分析、稀有疾病(癌症、帕金森综合症、奥兹海默症,等等)分析、金融风险建模和评估、市场系统性风险评估,等等。



 

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