On the Lp rates of convergence of simple linear rank statistics under contiguous alternatives

Abstract

This paper gives the rates of convergence for the L p , 1 ≤ p ≤ ∞, distances between the cumulative distribution functions of simple linear rank statistics and the normal random variables. It is shown that under contiguous alternatives the L 1 rate of convergence is O(n −δ 2 ) and the L p , 1 < p ≤ ∞, rate is O[n −δ 2 ( log n) (1+δ)/2] if the score generating function satisfies a Lipschitz condition of order δ, 0 < δ ≤ 1. The results of this paper improve and complement a number of known results.