## The Annals of Mathematical Statistics

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

### Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives

#### 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