The Annals of Mathematical Statistics

On Bounded Length Sequential Confidence Intervals Based on One-Sample Rank Order Statistics

Pranab Kumar Sen and Malay Ghosh

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Abstract

The problem of obtaining sequential confidence intervals for the median of an unknown symmetric distributon based on a general class of one-sample rank-order statistics is considered. It is shown that the usual one-sample rank-order statistic possesses the martingale or sub-martingale property according as the parent distribution is symmetric about the origin or not. Certain asymptotic almost sure convergence results (with specified order of convergence) for a class of rank-order processes and the empirical distribution are derived, and these are then utilized for the study of the properties of the proposed procedures.

Article information

Source
Ann. Math. Statist., Volume 42, Number 1 (1971), 189-203.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177693506

Digital Object Identifier
doi:10.1214/aoms/1177693506

Mathematical Reviews number (MathSciNet)
MR279939

Zentralblatt MATH identifier
0223.62100

JSTOR
links.jstor.org

Citation

Sen, Pranab Kumar; Ghosh, Malay. On Bounded Length Sequential Confidence Intervals Based on One-Sample Rank Order Statistics. Ann. Math. Statist. 42 (1971), no. 1, 189--203. doi:10.1214/aoms/1177693506. https://projecteuclid.org/euclid.aoms/1177693506


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