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统计推断Statistical inference机械部件通常被设计为精确地配合在一起。例如，如果一个轴被设计成在一个孔中 “滑动配合”，轴必须比孔小一点。(传统的公差可能表明，所有的尺寸都在这些预定的公差之内。然而，对实际生产的过程能力研究可能显示出具有长尾巴的正态分布）。轴和孔的尺寸通常会形成具有一些平均值（算术平均值）和标准差的正态分布。
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统计代写|统计推断作业代写Statistical inference代考|Arbuthnot’s and Gavarret’s Use of the Binomial
Actually, the idea of making a decision based on stochastic expectation became a possibility from the time the calculus of gambling came into being, and it was not long before that possibility was realized. Credit for the first “significance test” is given to John Arbuthnot (1710), who was also inventor, in a humorous pamphlet in 1712, of the archetypical Englishman John Bull (along with the Dutchman Nicholas Frog and the Frenchman Louis Baboon). Arbuthnot had written in the preface to his English translation of Huygens’ Rationiciis in Alea Ludo in 1692:
I believe the Calculation of the Quantity of Probability might be … applied to a great many Events which are accidental, besides those of games; . . . all the Politicks in the World are nothing else but a kind of Analysis of the Quantity of Probability in casual Events, and a good Politician signifies no more, but one who is dexterous at such calculations. (quoted in Pearson, 1978, p. 140)
Arbuthnot appears clearly here to hold the same vision of the scope of probability as James Bernoulli, whose book was still 21 years from publication. Arbuthnot’s contribution, also antedating de Moivre, was naturally what we would call nonparametric. As was mentioned in Chap. 2, Arbuthnot’s test, unsurprisingly for its time, was an argument for the existence of God; but it was surprisingly modern in form, and it provides an interesting prototype.
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|Probabilistic Criteria for the Rejection of Discordant Observations in Astronomy
The normal distribution had been used to model errors of measurement in astronomy, and the modern use of the probability integral over the tails of the distribution as the criterion in significance testing evolved from probabilistic criteria for the rejection of outlying observations. Sets of measurements assumed to arise from a normal process often contain deviations large enough to be suspected of having resulted from extraneous factors; and it is reasonable, if the normal law were to be retained, that errors actually arising from extraneous causes should be deleted in striking the average and in calculating the probable error. (The alternative would have been to assume a single operative process and to adopt a law giving greater probability to large deviations.) In cases where the observer had specific grounds for questioning the validity of a particular observation (e.g., seeing the assistant who made the observation stumble away from the telescope), there was of course no controversy. The challenging situation arose where the magnitude of the observation itself was the only basis for doubt, and here the practice of rejecting observations was hotly debated. To many, it smacked of fraud. Daniel Bernoulli was taking a dim view of the procedure in 1777 :
I see no way of drawing a dividing line between those that are to be utterly rejected and those that are to be wholly retained; it may even happen that the rejected observation is the one that would have supplied the best correction to the others. Nevertheless, I do not condemn in every case the principle of rejecting one or other of the observations, indeed I approve it, whenever in the course of observation an accident occurs which in itself raises an immediate scruple in the mind of the observer, before he has considered the event and compared it with the other observations. If there is no such reason for dissatisfaction I think each and every observation should be admitted whatever its quality, as long as the observer is conscious that he has taken every care. (translated by C. G. Allen, in Kendall, 1961, p. 3)
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|The Normal Model and Data in the Social Sciences
Although Peirce’s rejection scheme is recognizable as the original use of the tail integral, the normal model had meanwhile been transplanted to sociological data, and the idea was independently developing in that area of tests of discrepancy between model and data. The idea came slowly, however.
One early example was due to Robert Campbell (1859), whose article was inspired by Henry Thomas Buckle’s History of Civilization in England, published 2 years earlier. Porter (1986) describes Buckle as “possibly the most enthusiastic and beyond doubt the most influential popularizer of Quetelet’s ideas on statistical regularity” (p. 65). Buckle saw in Quetelet’s work support for the ascendant doctrine of classical liberalism: The social laws that were revealed by statistical regularities demanded for their smooth operation an absence of forcible intervention by government. Campbell thought the stability of some of these series ought to be tested. He devised a multinomial test for suicide data-though, as Stigler (1986) notes, without drawing any conclusions. He described his procedure as follows:
We started with the hypothesis that we knew nothing about the laws regulating the phaenomena and causing either uniformity or variety. Now this hypothesis was morally incorrect in this respect. For we knew this at starting, that such laws may exist; and if the degree of uniformity or the reverse in the real tables present a striking contrast to that which we should expect from the result of our hypothesis, we may fairly be led to the conclusion that such laws do exist, and that our tables justify us in looking for causes to explain their remarkable features. (Campbell, 1859, p. 366)
统计推断学代写
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|ARBUTHNOT’S AND GAVARRET’S USE OF THE BINOMIAL
实际上，基于随机期望做决定的想法，从赌算出现的时候就已经成为一种可能，而且不久之后这种可能性就实现了。第一次“显着性检验”的功劳归功于 John Arbuthnot1710，他也是 1712 年在一本幽默小册子中发明了典型的英国人约翰·布尔一种一世这nG在一世吨H吨H和D你吨CH米一种nñ一世CH这一世一种sFr这G一种nd吨H和Fr和nCH米一种n大号这你一世s乙一种b这这n. Arbuthnot 在 1692 年在 Alea Ludo 的 Huygens 的 Rationiciis 英文译本的序言中写道：
我相信概率量的计算可能……适用于许多偶然的事件，除了游戏事件；. . . 世界上所有的政治不过是对偶然事件中概率数量的一种分析，一个好的政治家并不意味着什么，而是一个精通这种计算的人。q你这吨和d一世n磷和一种rs这n,1978,p.140
Arbuthnot 在这里显然与詹姆斯·伯努利（James Bernoulli）持有相同的概率范围愿景，后者的书距离出版还有 21 年。Arbuthnot 的贡献，也早于 de Moivre，自然就是我们所说的非参数。正如第一章中提到的那样。2，阿布斯诺特的测试，在当时毫不奇怪，是对上帝存在的论证；但它的形式令人惊讶地现代，它提供了一个有趣的原型。
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|PROBABILISTIC CRITERIA FOR THE REJECTION OF DISCORDANT OBSERVATIONS IN ASTRONOMY
正态分布已被用于模拟天文学中的测量误差，而现代使用分布尾部的概率积分作为显着性检验的标准是从拒绝异常观测的概率标准演变而来的。假设来自正常过程的测量值集通常包含大到足以怀疑是由外来因素引起的偏差；如果要保留正常规律，那么在计算平均数和计算可能的错误时，应该删除实际由外在原因引起的错误，这是合理的。吨H和一种一世吨和rn一种吨一世v和在这你一世dH一种v和b和和n吨这一种ss你米和一种s一世nG一世和这p和r一种吨一世v和pr这C和ss一种nd吨这一种d这p吨一种一世一种在G一世v一世nGGr和一种吨和rpr这b一种b一世一世一世吨是吨这一世一种rG和d和v一世一种吨一世这ns.在观察者有特定理由质疑特定观察的有效性的情况下和.G.,s和和一世nG吨H和一种ss一世s吨一种n吨在H这米一种d和吨H和这bs和rv一种吨一世这ns吨你米b一世和一种在一种是Fr这米吨H和吨和一世和sC这p和，当然没有争议。具有挑战性的情况出现了，观察本身的大小是唯一怀疑的基础，这里对拒绝观察的做法进行了激烈的辩论。对许多人来说，它带有欺诈的味道。丹尼尔·伯努利在 1777 年对这个程序的看法很模糊：
我看不出有什么办法可以在完全拒绝的人和完全保留的人之间划清界限。甚至可能会发生被拒绝的观察是可以为其他观察提供最佳校正的观察。尽管如此，我并不在任何情况下都谴责拒绝一个或另一个观察的原则，实际上我赞成它，只要在观察过程中发生事故，它本身就会在观察者的头脑中引起直接的顾忌，在他之前已经考虑了该事件并将其与其他观察结果进行了比较。如果没有这种不满意的理由，我认为每一个观察都应该被承认，无论它的质量如何，只要观察者意识到他已经采取了一切措施。吨r一种ns一世一种吨和db是C.G.一种一世一世和n,一世n到和nd一种一世一世,1961,p.3
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|THE NORMAL MODEL AND DATA IN THE SOCIAL SCIENCES
尽管皮尔士的拒绝方案被认为是尾积分的原始用途，但同时正态模型已被移植到社会学数据中，并且该想法在模型与数据差异检验领域独立发展。然而，这个想法来得很慢。
一个早期的例子是由于罗伯特坎贝尔1859，其文章的灵感来自于 2 年前出版的亨利·托马斯·巴克尔 (Henry Thomas Buckle) 的《英格兰文明史》。搬运工1986将 Buckle 描述为“可能是 Quetelet 关于统计规律的思想最热情、最有影响力的推广者”p.65. Buckle 在 Quetelet 的著作中看到了对占主导地位的古典自由主义学说的支持：统计规律揭示的社会规律要求其平稳运行，无需政府的强制干预。Campbell 认为应该测试其中一些系列的稳定性。他设计了一个针对自杀数据的多项式检验——不过，正如 Stigler1986注释，不得出任何结论。他将他的程序描述如下：
我们从假设开始，即我们对调节现象和导致统一性或多样性的规律一无所知。现在这个假设在这方面在道德上是不正确的。因为我们一开始就知道，这样的规律可能存在；如果真实表格中的一致性程度或相反程度与我们从假设结果中预期的结果形成鲜明对比，我们可以公平地得出这样的结论，即这些规律确实存在，并且我们的表格证明了我们的合理性在寻找原因来解释它们的显着特征。C一种米pb和一世一世,1859,p.366
统计代写|统计推断作业代写STATISTICAL INFERENCE代考 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。
