The Annals of Statistics

The Invariance Principle for One-Sample Rank-Order Statistics

Pranab Kumar Sen

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Abstract

Analogous to the Donsker theorem on partial cumulative sums of independent random variables, for a broad class of one-sample rank order statistics, weak convergence to Brownian motion processes is studied here. A simple proof of the asymptotic normality of these statistics for random sample sizes is also presented. Some asymptotic results on renewal theory for one-sample rank order statistics are derived.

Article information

Source
Ann. Statist., Volume 2, Number 1 (1974), 49-62.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342612

Digital Object Identifier
doi:10.1214/aos/1176342612

Mathematical Reviews number (MathSciNet)
MR345309

Zentralblatt MATH identifier
0273.60005

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 62G99: None of the above, but in this section

Keywords
Brownian motion processes invariance principles martingales one-sample rank order statistics random sample sizes renewal theory weak convergence

Citation

Sen, Pranab Kumar. The Invariance Principle for One-Sample Rank-Order Statistics. Ann. Statist. 2 (1974), no. 1, 49--62. doi:10.1214/aos/1176342612. https://projecteuclid.org/euclid.aos/1176342612


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Corrections

  • See Correction: Pranab Kumar Sen. Notes: Correction to "The Invariance Principle for One-Sample Rank-Order Statistics". Ann. Statist., Volume 2, Number 6 (1974), 1358--1358.