The Annals of Mathematical Statistics

Some Basic Theorems of Distribution-Free Statistics

C. B. Bell

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The object of this article is the analysis of the concept of distribution-freeness. In Section 2 the common types of distribution-free (DF) statistics are defined and related. In Section 3 a generalization of the invariance principle is employed to construct DF statistics for classes of cpfs generated by groups of transformations of the sample space. It is shown in Section 4 that a function of several DF statistics is not necessarily DF, but that independence guarantees the desired result. The existence of a DF statistic is shown, in Section 5, to be equivalent to the existence of a suitable partition of the sample space. Several open problems are mentioned in Section 6, the final section.

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Ann. Math. Statist., Volume 35, Number 1 (1964), 150-156.

First available in Project Euclid: 27 April 2007

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Bell, C. B. Some Basic Theorems of Distribution-Free Statistics. Ann. Math. Statist. 35 (1964), no. 1, 150--156. doi:10.1214/aoms/1177703736.

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