On finite sequences of real numbers
On finite sequences of real numbers
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DOI：
10.1098/rspa.1931.0209
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发表时间：
1931-12-01
期刊：
影响因子：
--
通讯作者：
Heywood, HB
中科院分区：
文献类型：
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作者：
Heywood, HB
统计科学的材料主要由有限的数集组成，因为它们是按顺序记录的，所以是序列。它们可以被看作是它们的元素的秩的函数，关于真实的函数的定理也适用于它们。特别地，它们能够进行正交或其他划分，能够类似于级数展开和变换地展开;这些序列的集合同样可以进行替换。这些考虑使统计理论的某些部分符合一般数学理论，并提出了有趣的可能性。斯皮尔曼在其智力研究中提出的所谓“因素”理论，近年来变得十分重要。它是偏相关理论的产物。从数学上讲，序列的“因子”是由正交划分产生的分量，正交序列是具有零相关性的序列。在考虑测量序列的“因子”或其他成分在多大程度上代表物理现实时，统计学家必须仔细研究分布和抽样问题，但是从上面所说的可以看出，序列的划分和发展的一般理论，这是本文的主题，不涉及这些问题。在《自然》杂志上的一封信中对这种方法的应用进行了简要的讨论，其中指出了以下结果。
The material of the science of statistics consists in the main of finite sets of numbers, which, since they are recorded in order, are sequences. They may be regarded as functions of the rank of their elements, and theorems concerning real functions hold good for them. In particular they are capable of partition, orthogonal or other, of development analogous to expansion in series and of transformation; sets of such sequences may likewise be subjected to substitution. These considerations bring certain parts of the theory of statistics into line with general mathematical theory and suggest interesting possibilities. The so-called theory of “ factors,” put forward by Spearman in connection with his researches into intelligence, has become very important in recent years. It is an outgrowth of the theory of partial correlation. Mathematically speaking the “factors” of a sequence are components resulting from orthogonal partition, orthogonal sequences being those which have zero correlation. In considering how far the “factors” or other components of a sequence of measurements represent physical realities, the statistician has to make a careful study of questions of distribution and sampling, but from what has been said it will be seen that the general theory of the partition and development of sequences, which is the subject of this paper, does not involve these questions. A brief discussion of the application of this method was given in a letter in ‘Nature’ in which the following results were indicated.