비모수적 순위 검정 통계량의 불편성에 관한 연구

Abstract

Lehmann(1959,1986) showed that one-sided wilcoxon rank test is unbiased against at location parameter family of distributions. But he raised the question of two-sided wilcoxon rank test is biased. Then Sugiura(1965) showed that two-sided wilcoxon rank test for different sizes is biased against a location parameter family of distributions by giving a counter example. Sugiura, etal.(2006) showed that the two-sided wilcoxon rank test for equal sample sizes is biased against a location parameter family of distributions by giving a counter example. But it is restricted that sample size is 2. In this paper, we have found another counterexample of Sugiura, etal.(2006). For scale parameters, we have considered Ansari-Bradley test and showed that Ansari-Bradley test for different sample sizes is unbiased against a scale parameter family of distributions by giving a counter example.