A Large Deviations Result and Bahadur Efficiency of Two-Sample Tests Based on One-Sample Sign Statistics.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK DEPT OF STATISTICS
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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 Moods test. All solutions have the same Pitman efficiency. This paper shows that the choices can be distinguished on the basis of Bahadurs efficiency. We formulate the problem in terms of asymptotically fixed-width confidence intervals. In this context various median tests including Moods 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 Moods test is recommended. Author
- Statistics and Probability