On Some Useful "Inefficient" Statistics
On Some Useful "Inefficient" Statistics
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DOI：
10.1007/978-0-387-44956-2_4
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发表时间：
1946-12
影响因子：
--
通讯作者：
F. Mosteller
中科院分区：
文献类型：
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作者：
F. Mosteller
有几种统计技术可以通过穿孔卡片设备来经济地分析大量数据;这些技术中的大多数只需要一个计数分类器。所提出的方法是专门为数据便宜的情况下相比，通过统计“有效“或“最强大的”程序的分析成本。主要的技术是使用顺序统计量的函数，我们称之为系统统计量。证明了某些顺序统计量是按正态多元律渐近联合分布的。对于从正态分布变量中抽取的大样本，我们描述并给出了快速方法的效率：i）通过使用1，2，10，10适当选择的顺序统计量来估计均值;（cf. ii）通过使用2、4或8个适当选择的顺序统计量来估计标准差;第89页）iii）用于估计相关系数，无论正态二元分布的其他参数是否已知（涉及三个排序和三个计数操作）（参见第94页）。将程序ii）和iii）的效率与不涉及平方和或乘积的其他估计的效率进行比较。
Several statistical techniques are proposed for economically analyzing large masses of data by means of punched-card equipment; most of these techniques require only a counting sorter. The methods proposed are designed especially for situations where data are inexpensive compared to the cost of analysis by means of statistically “efficient”or “most powerful” procedures. The principal technique is the use of functions of order statistics, which we callsystematic statistics.It is demonstrated that certain order statistics are asymptotically jointly distributed according to the normal multivariate law.For large samples drawn from normally distributed variables we describe and give the efficiencies of rapid methods:i)for estimating the mean by using 1, 2,⋯, 10 suitably chosen order statistics; (cf. p. 86)ii)for estimating the standard deviation by using 2, 4, or 8 suitably chosen order statistics; (cf. p. 89)iii)for estimating the correlation coefficient whether other parameters of the normal bivariate distribution are known or not (three sorting and three counting operations are involved) (cf. p. 94).The efficiencies of procedures ii) and iii) are compared with the efficiencies of other estimates which do not involve sums of squares or products.