A modified Wilcoxon signed rank test for shift in location

Abstract

Test statistics having scores which emphasize extreme observations and hence are effective in detecting a shift in location in light tailed distributions were proposed by Randles and Hogg (1973). While for heavy tailed distributions, statistics that downweight extreme observations are developed by Pollicello (1978). A Modified Wilcoxon signed rank statistic for shift in location is proposed. It is based on modifying the Wilcoxon scores according to the distributions’s tail lengths. The extreme scores are determined according to the distribution’s tail lengths estimated from the sample. For light tailed distributions, it emphasizes extrema observations by pushing up their scores. While for heavy tailed distributions it downweights the scores of extreme observations. In this sense it is a continuously adaptive test. The proposed test is compared, through a simulation study, with the Wilcoxon signed rank test and the sign test. The results show that the proposed test has a better power performance than the other tests in almost all situations considered.