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高斯与最小二乘法的发明AI 解读

The most famous priority dispute in the history of statistics is that between Gauss and Legendre, over the discovery of the method of least squares. New evidence, both documentary and statistical, is discussed, and an attempt is made to evaluate Gauss's claim. It is argued (though not conclusively) that Gauss probably possessed the method well before Legendre, but that he was unsuccessful in communicating it to his contemporaries. Data on the French meridian arc are…

一个 Edgeworth 奇例AI 解读

Taking the sample mean of a set of measurements need not be uniformly advantageous, even when $n = 2$ and all moments are finite. The examples presented include one given by Edgeworth in 1883.

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稳健估计量在真实数据中有效吗？AI 解读

Most studies of robust estimators of location parameters have relied upon mathematical theory, computer simulated data, or a combination of these. This paper presents a comparison of the performances of eleven estimators using real data sets. Twenty sets of data from 1761 determinations of the parallax of the sun, from 1798 measurements of the mean density of the earth, and from circa 1880 measurements of the speed of light, are employed in the study, with the current values…

分数阶次序统计量及其应用AI 解读

Based upon Ferguson's Dirichlet process, we introduce an order-statistic process, a technical device which may be viewed as defining a continuum of fractional order statistics for any sample size. The order-statistic process provides an alternative to the quantile function essentially based on stochastic rather than linear interpolation. Its use in large-sample theory is suggested, and a simple proof is given that the order-statistic process, suitably normalized, converges…

八个世纪的抽样检验：钱币检验仪式AI 解读

A sampling inspection scheme bearing striking similarities to modern procedures has been in more or less continuous operation at the Royal Mint in London for about eight centuries. The history of this scheme is reviewed, and a defect in the manner in which the critical levels were set is noted. The possibility that Master of the Mint, Isaac Newton might have grasped the nature of the defect is discussed. Finally, we review the situation at the United States Mint, where…

八个世纪的抽样检验：铸币验金仪式AI 解读

A sampling inspection scheme bearing striking similarities to modern procedures has been in more or less continuous operation at the Royal Mint in London for about eight centuries. The history of this scheme is reviewed, and a defect in the manner in which the critical levels were set is noted. The possibility that Master of the Mint, Isaac Newton might have grasped the nature of the defect is discussed. Finally, we review the situation at the United States Mint, where…

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具有光滑权函数的次序统计量线性函数AI 解读

This paper considers linear functions of order statistics of the form $S_n = n^{-1} \sum J(i/(n + 1))X_{(i)}$. The main results are that $S_n$ is asymptotically normal if the second moment of the population is finite and $J$ is bounded and continuous a.e. $F^{-1}$, and that this first result continues to hold even if the unordered observations are not identically distributed. The moment condition can be discarded if $J$ trims the extremes. In addition, asymptotic formulas…

Simon Newcomb、Percy Daniell 与稳健估计史：1885—1920AI 解读

This article reviews some of the history of robust estimation, emphasizing the period 1885–1920 and the work of Newcomb, Edgeworth, Sheppard, and Daniell. Particular attention is paid to lines of development which have excited recent interest, including linear functions of order statistics and mixtures of normal densities as models for heavy-tailed populations.

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截尾均值的渐近分布AI 解读

In this paper it is shown that in order for the trimmed mean to be asymptotically normal, it is necessary and sufficient that the sample be trimmed at sample percentiles such that the corresponding population percentiles are uniquely defined. (The sufficiency of this condition is well known.) In addition, the (non-normal) limiting distribution of the trimmed mean when this condition is not satisfied is derived, and it is shown that in some situations the use of the trimmed…

分枝过程灭绝概率及相关参数的估计AI 解读

Maximum likelihood estimates of the probability of the eventual extinction of a possibly age-dependent branching process are given for both the parametric and nonparametric cases, and their asymptotic properties derived. It is found that the nonparametric estimate performs very well relative to the parametric estimate in a large variety of situations, and therefore would often be preferable to the parametric estimate in view of the latter's lack of robustness.

多项式回归的最优实验设计AI 解读

The problem of choosing the optimal design to estimate a regression function which can be well-approximated by a polynomial is considered, and two new optimality criteria are presented and discussed. Use of these criteria is illustrated by a detailed discussion of the case that the regression function can be assumed approximately linear. These criteria, which can be considered as compromises between the incompatible goals of inference about the regression function under an…

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利用随机分配控制选择偏差AI 解读

In comparing two treatments, suppose the suitable subjects arrive sequentially and must be treated at once. In such situations, if the experiment calls for fixed treatment numbers, the experimenter can, using his knowledge of the number of treatments that have been assigned, bias the experiment by his selection of subjects. If we consider the method of assigning treatments as an experimental design, Blackwell & Hodges (1957) have shown that the minimax design is the…