A Bahadur efficiency comparison between one and two sample rank statistics and their sequential rank statistic analogues
Let \(Z_ 1,Z_ 2,..\). be a sequence of i.i.d. random variables and \(R_{in}\) the rank of \(Z_ i\) among \(Z_ 1,...,Z_ n\). Let further \(J_ n(i/(n+1))\) be scores, \(c_{in}\) given regression numbers and \(\bar c_{in}=\sum^{i-1}_{j=1}c_{jn}/(i-1)\). The author compares statistical properties of the test statistic \(T_ n=\sum^{n}_{i=1}c_{in}J_ n(R_{in}/(n+1))\) and its sequential analogue \(M_ n=\sum^{n}_{i=1}(c_{in}-\bar c_{in})J_ i(R_{ii}/(i+1)).\) It is known from the author's paper in Ann. Stat. 9, 424-436 (1981; Zbl 0459.62015) that both statistics have the same Pitman efficiency against local alternatives. The main result of this paper is that in the Bahadur sense both statistics show different efficiency properties. A similar result is established for signed-rank procedures.
Pitman efficiency against local alternatives
scientific article; zbMATH DE number 3850295