本文選題：統(tǒng)計歷史　切入點：小樣本理論　出處：《天津財經(jīng)大學(xué)》2014年碩士論文

【摘要】：讀史明智,以史為鑒。任何一門學(xué)科的前進與發(fā)展都離不開研究者對其歷史的深入研究,因此史學(xué)研究的重要性是毋庸置疑的。統(tǒng)計學(xué)是一門與現(xiàn)代科學(xué)緊密聯(lián)系的學(xué)科,也是一門積累性很強的學(xué)科,其理論和方法都具有延續(xù)性,更需要統(tǒng)計學(xué)者為其歷史的研究做出努力。20世紀(jì)前30年是現(xiàn)代統(tǒng)計學(xué)理論形成過程中的一個非常重要的歷史階段。在此期間,以Gosset和Fisher為代表的英國統(tǒng)計學(xué)家在統(tǒng)計學(xué)領(lǐng)域掀起了一場小樣本理論的革命。這場革命的背景是,隨著科學(xué)與技術(shù)的快速發(fā)展,在人工控制試驗條件下所產(chǎn)生的統(tǒng)計數(shù)據(jù)分析問題已不再適用于傳統(tǒng)的以中心極限定理為理論依據(jù)的大樣本方法。Gosset于1908年提出的“學(xué)生”分布標(biāo)志著小樣本理論的正式奠基。之后,Fisher從Gosset手中接過小樣本理論的大旗,推導(dǎo)出了諸如樣本方差、樣本相關(guān)系數(shù)、樣本偏相關(guān)系數(shù)、樣本復(fù)相關(guān)系數(shù)等一系列重要統(tǒng)計量的精確分布。Fisher的這些成就不僅使其本人成為當(dāng)代毫無爭議的統(tǒng)計學(xué)界的領(lǐng)袖,而且也使小樣本理論得以迅速地度過草建時期。正如著名的統(tǒng)計學(xué)家Savage所言：“仰仗著推導(dǎo)精確抽樣分布的高超技巧,Fisher將統(tǒng)計學(xué)帶出了它的‘嬰兒時期’,他在這方面的技巧也從未被人超越過”。Savage所指的“技巧”正是陳希孺先生所說的“n維幾何法”。論文在參考大量原始文獻的基礎(chǔ)上,以小樣本理論的起源為背景,對Fisher的“n維幾何法”進行了詳細的解讀,并對其在一些重要樣本統(tǒng)計量分布上的應(yīng)用以及影響進行了介紹,希望能夠為拓展人們解決統(tǒng)計量分布問題的思路提供幫助。
[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 The problem of statistical data analysis under the condition of manual control experiment is no longer applicable to the traditional large sample method based on the central limit theorem.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.
【學(xué)位授予單位】：天津財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：C81

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1 李明明;Fisher與小樣本及“n維幾何法”[D];天津財經(jīng)大學(xué);2014年

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