Cram�r type large deviations for simple linear rank statistics

Abstract

A Cramer type large deviation theorem for simple linear rank statistics is obtained (range \(0 < x < {}_0(N^{{1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-\nulldelimiterspace} 6}} )\)). The method of proof consists in approximating the simple linear rank statistic by a sum of independent, uniformly bounded random variables and then applying a Cramer type large deviation theorem on this sum.