Open Access
December, 1970 On Some Convergence Properties of One-Sample Rank Order Statistics
Pranab Kumar Sen
Ann. Math. Statist. 41(6): 2140-2143 (December, 1970). DOI: 10.1214/aoms/1177696716


For a broad class of one-sample rank order statistics, almost sure (a.s.) convergence and exponential bounds for the probability of large deviations, when the basic random variables are not necessarily identically distributed, are established here. In this context, extending a result of Brillinger (1962) to the case of non-iidrv (independent and identically distributed random variables), a result on the a.s. convergence of sample means for a double sequence of random variables is derived. These results are of importance for the study of the properties of sequential tests and estimates based on rank order statistics.


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Pranab Kumar Sen. "On Some Convergence Properties of One-Sample Rank Order Statistics." Ann. Math. Statist. 41 (6) 2140 - 2143, December, 1970.


Published: December, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0216.22101
MathSciNet: MR267712
Digital Object Identifier: 10.1214/aoms/1177696716

Rights: Copyright © 1970 Institute of Mathematical Statistics

Vol.41 • No. 6 • December, 1970
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