On the Centering of a Simple Linear Rank Statistic
On the Centering of a Simple Linear Rank Statistic
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 …