A rank statistic for the change-point problem and its application

Abstract

The rank statistic for a location-scale parameter is introduced to a change-point problem. A combination of the Wilcoxon and Mood statistics is extended to the change-point context. The proposed rank statistic is used to detect a change-point in a setting involving at most one change in this paper. The limiting distribution of the suggested statistic is derived under the null hypothesis (no change). The finite sample critical value of the suggested statistic is estimated by simulation studies. In addition, the accuracy of detecting a change-point is investigated by simulation studies. The method is illustrated by the analysis of various data.