Open Access
March, 1964 Some Basic Theorems of Distribution-Free Statistics
C. B. Bell
Ann. Math. Statist. 35(1): 150-156 (March, 1964). DOI: 10.1214/aoms/1177703736


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.


Download Citation

C. B. Bell. "Some Basic Theorems of Distribution-Free Statistics." Ann. Math. Statist. 35 (1) 150 - 156, March, 1964.


Published: March, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0136.40502
MathSciNet: MR158480
Digital Object Identifier: 10.1214/aoms/1177703736

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 1 • March, 1964
Back to Top