Fisher与小样本及“n维几何法”

发布时间：2018-03-24 07:22

本文选题：统计历史　切入点：小样本理论　出处：《天津财经大学》2014年硕士论文

【摘要】：读史明智,以史为鉴。任何一门学科的前进与发展都离不开研究者对其历史的深入研究,因此史学研究的重要性是毋庸置疑的。统计学是一门与现代科学紧密联系的学科,也是一门积累性很强的学科,其理论和方法都具有延续性,更需要统计学者为其历史的研究做出努力。20世纪前30年是现代统计学理论形成过程中的一个非常重要的历史阶段。在此期间,以Gosset和Fisher为代表的英国统计学家在统计学领域掀起了一场小样本理论的革命。这场革命的背景是,随着科学与技术的快速发展,在人工控制试验条件下所产生的统计数据分析问题已不再适用于传统的以中心极限定理为理论依据的大样本方法。Gosset于1908年提出的“学生”分布标志着小样本理论的正式奠基。之后,Fisher从Gosset手中接过小样本理论的大旗,推导出了诸如样本方差、样本相关系数、样本偏相关系数、样本复相关系数等一系列重要统计量的精确分布。Fisher的这些成就不仅使其本人成为当代毫无争议的统计学界的领袖,而且也使小样本理论得以迅速地度过草建时期。正如著名的统计学家Savage所言：“仰仗着推导精确抽样分布的高超技巧,Fisher将统计学带出了它的‘婴儿时期’,他在这方面的技巧也从未被人超越过”。Savage所指的“技巧”正是陈希孺先生所说的“n维几何法”。论文在参考大量原始文献的基础上,以小样本理论的起源为背景,对Fisher的“n维几何法”进行了详细的解读,并对其在一些重要样本统计量分布上的应用以及影响进行了介绍,希望能够为拓展人们解决统计量分布问题的思路提供帮助。
[Abstract]:Reading history is wise and learning from history. The progress and development of any subject can not be separated from the in-depth study of its history by researchers, so the importance of historical research is beyond doubt. Statistics is a discipline closely related to modern science. It is also a highly accumulative discipline whose theories and methods have continuity. The first 30 years of the 20th century is a very important historical stage in the formation of modern statistical theory. British statisticians, represented by Gosset and Fisher, revolutionized small-sample theory in the field of statistics against the backdrop of rapid advances in science and technology. The problem of statistical data analysis under the condition of manual control experiment is no longer applicable to the traditional large sample method based on the central limit theorem. The "student" distribution proposed by Gosset in 1908 marks the small sample theory. After which Fisher took the banner of small sample theory from Gosset. The exact distribution of a series of important statistics, such as sample variance, sample correlation coefficient, sample partial correlation coefficient, sample complex correlation coefficient and so on, are derived. Fisher's achievements not only make him a leader in the contemporary undisputed statistical field. It also allowed the theory of small samples to get through the grass very quickly. As the famous statistician Savage put it: "he brought statistics out of its infancy, relying on the skilful skill of deducing accurate sampling distribution... The technique of face has never been surmounted by anyone. "Savage means" skill "is exactly what Mr. Chen Xiru calls" n-dimensional geometry. "the paper is based on a large number of original documents." Based on the origin of small sample theory, the "n-dimensional geometric method" of Fisher is interpreted in detail, and its application and influence in the distribution of some important sample statistics are introduced. It is hoped that it can help people to solve the problem of statistical distribution.
【学位授予单位】：天津财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：C81

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