The Annals of Statistics

A Law of Iterated Logarithm for One-Sample Rank Order Statistics and an Application

Pranab Kumar Sen and Malay Ghosh

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Abstract

For one sample rank order statistics, a law of iterated logarithm and almost sure convergence to Wiener processes are established here. For the one-sample location problem, a sequential test procedure based on rank order statistics is proposed, and with the aid of the earlier results, it is shown that this has power one and arbitrarily small type I error.

Article information

Source
Ann. Statist., Volume 1, Number 3 (1973), 568-576.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342426

Digital Object Identifier
doi:10.1214/aos/1176342426

Mathematical Reviews number (MathSciNet)
MR365887

Zentralblatt MATH identifier
0258.60023

JSTOR
links.jstor.org

Subjects
Primary: 60F10: Large deviations
Secondary: 60F15: Strong theorems 62G99: None of the above, but in this section

Keywords
Almost sure convergence to Wiener processes law of iterated logarithm probability of moderate deviations sequential test with power one rank order statistics

Citation

Sen, Pranab Kumar; Ghosh, Malay. A Law of Iterated Logarithm for One-Sample Rank Order Statistics and an Application. Ann. Statist. 1 (1973), no. 3, 568--576. doi:10.1214/aos/1176342426. https://projecteuclid.org/euclid.aos/1176342426


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