Zhaoyuan Li, Maozai Tian

【Abstract】

It`s well-known that change-point problem is an important part of model statistical analysis. Most of the existing methods are not robust to criteria of the evaluation of change-point problem. In this article, we consider "mean-shift" problem in change-point studies. A quantile test of single quantile is proposed based on saddlepoint approximation method. In order to utilize the information at different quantile of the sequence, we further construct a "composite quantile test" to calculate the probability of every location of the sequence to be a change-point. The location of change-point can be pinpointed rather than estimated within a interval. The proposed tests make no assumptions about the functional forms of the sequence distribution and work sensitively on both large and small size samples, the case of change-point in the tails, and multiple change-points situation. The good performances of the tests are confirmed by simulations and real data analysis. The saddlepoint approximation based distribution of the test statistic that is developed in the paper is of independent interest and appealing. This finding may be of independent interest to the readers in this research area.

【Keywords】

change-point, mean shift, saddlepoint approximations, composite quantile, bootstrap