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January, 1973 On the Centering of a Simple Linear Rank Statistic
Wassily Hoeffding
Ann. Statist. 1(1): 54-66 (January, 1973). DOI: 10.1214/aos/1193342381


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.


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Wassily Hoeffding. "On the Centering of a Simple Linear Rank Statistic." Ann. Statist. 1 (1) 54 - 66, January, 1973.


Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0255.62015
MathSciNet: MR362689
Digital Object Identifier: 10.1214/aos/1193342381

Primary: 62G10
Secondary: 60F05

Keywords: asymptotically normal , centering constant , Simple linear rank statistic

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 1 • January, 1973
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