Large Deviations Result and Bahadur Efficiency of Two-Sample Tests Based on One-Sample Sign Statistics

摘要

This paper discusses the two-sample test of location based on the comparison of two distribution free one-sample confidence intervals derived from sign statistics. This test procedure, first introduced by Hettmansperger (1986), rejects the null hypothesis of equal population medians when the two intervals are disjoint. He presents three different ways to select the two one-sample intervals and one choice leads to Mood's test. All solutions have the same Pitman efficiency. This paper shows that the choices can be distinguished on the basis of Bahadur's efficiency. We formulate the problem in terms of (asymptotically) fixed-width confidence intervals. In this context various median tests (including Mood's test) arise as special cases and they yield different performance. The solution that specifies equal asymptotic lengths for the one-sample intervals (which is different from Mood's test) is recommended. (Author)