The Annals of Mathematical Statistics

Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives

Hira Lal Koul

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Abstract

In this paper two convergence theorems are proved. One gives a strong law of large numbers for a class of linear rank statistics and the other gives weak convergence of a weighted empirical cumulative process to Gaussian process, concentrated on continuous sample functions. Of course, both of these results are true under some regularity condition on the quantities involved.

Article information

Source
Ann. Math. Statist., Volume 41, Number 5 (1970), 1768-1773.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177696824

Digital Object Identifier
doi:10.1214/aoms/1177696824

Mathematical Reviews number (MathSciNet)
MR267631

Zentralblatt MATH identifier
0232.62020

JSTOR
links.jstor.org

Citation

Koul, Hira Lal. Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives. Ann. Math. Statist. 41 (1970), no. 5, 1768--1773. doi:10.1214/aoms/1177696824. https://projecteuclid.org/euclid.aoms/1177696824


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