The Annals of Statistics

On the Centering of a Simple Linear Rank Statistic

Wassily Hoeffding

Full-text: Open access


Hajek (1968) proved that under weak conditions the distribution of a simple linear rank statistic $S$ is asymptotically normal, centered at the mean $ES$. He left open the question whether under the same conditions the centering constant $ES$ may be replaced by a simpler constant $\mu$, as was found to be true in the two-sample case and under different conditions by Chernoff and Savage (1958) and Govindarajulu, LeCam and Rhagavachari (1966). In this paper it is shown that the replacement of $ES$ by $\mu$ is permissible if one of Hajek's conditions is slightly strengthened.

Article information

Ann. Statist., Volume 1, Number 1 (1973), 54-66.

First available in Project Euclid: 25 October 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing
Secondary: 60F05: Central limit and other weak theorems

Simple linear rank statistic asymptotically normal centering constant


Hoeffding, Wassily. On the Centering of a Simple Linear Rank Statistic. Ann. Statist. 1 (1973), no. 1, 54--66. doi:10.1214/aos/1193342381.

Export citation