Properties of sufficiency and statistical tests
Properties of sufficiency and statistical tests
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DOI：
10.1098/rspa.1937.0109
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发表时间：
1937-05-01
影响因子：
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通讯作者：
Bartlett, MS
中科院分区：
文献类型：
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作者：
Bartlett, MS
在之前的一篇文章中，在讨论小样本统计理论中充分性的重要性时，主要关注的是估计理论。本文进一步讨论了小样本检验的结构，这些检验是否与估计和基准分布问题有关，或者是否具有拟合优度检验的性质。与前面一样，符号|表示变量是由给定的b值限定的。固定变量可以用bbbbb表示，类似地，如果从上下文中可以清楚地看出，bbbbb可以简单地写成|。对应于Fisher在单个未知θ情况下引入的辅助信息思想，其中辅助统计量控制我们估计的准确性，如果其分布满足“充分性”并且包含θ上的所有信息，我将形式为t |的条件统计量称为准充分统计量。在其他未知的更一般的情况下，这样的统计量可能包含关于θ的所有可用信息。
1—In a previous paper, dealing with the importance of properties of sufficiency in the statistical theory of small samples, attention was mainly confined to the theory of estimation. In the present paper the structure of small sample tests, whether these are related to problems of estimation and fiducial distributions, or are of the nature of tests of goodness of fit, is considered further. The notationa|bimplies as before that the variateais conditioned by a given value ofb. The fixed variatebmay be denoted by |b, and analogously ifbis clear from the context,a|bmay be written simply asa|. Corresponding to the idea of ancillary information introduced by Fisher for the case of a single unknownθ, where auxiliary statistics control the accuracy of our estimate, I have termed a conditional statistic of the formT|, quasi-sufficient, if its distribution satisfies the “sufficiency” property and contains all the information onθ. In the more general case of other unknowns, such a statistic may contain all theavailableinformation onθ.