A Note on the Wilcoxon Score for the One-Sample Problem

• 발행기관: 한국자료분석학회
• 저자명: 박정섭(Jung-Sub Park)
• 간행물 정보: 『Journal of The Korean Data Analysis Society (JKDAS)』Vol.17 No.2, 623~629쪽, 전체 7쪽
• 주제분류: 자연과학 > 통계학
• 파일형태: PDF
• 발행일자: 2015.04.30

영문 초록

In this study, we consider to unify the sign and signed-rank tests for the one-sample problem by introducing the score functions. In this approach, we propose a generalization of the signed-rank statistics for the one-sample case. Then we derive the asymptotic normality of the proposed statistics using the large sample approximation theorem for the real application to the problem. For this purpose, we use the Liapounov central limit theorem, which requires the higher moments than the second moment. Then we compare the efficiency between the proposed test and the existed rank-sum tests by using the generalization form of the score function by obtaining empirical powers through a simulation study. We consider the three different sample sizes and four kinds of underlying distributions for this comparison study. Finally, we discuss the some useful aspect of median and comment briefly on the resampling methods for the derivation of the null distributions for any given nonparametric statistics.

목차

1. Introduction

2. A generalization of Wilcoxon signed-rank test

3. Simulation study

4. Some concluding remarks

References

키워드

One-sample problem Nonparametric tests Liapounov central limit theorem Median