An Adaptive Test for Change in Level at an Unknown Time Point

We consider the problem of testing whether there exists a change in level at an unknown time point when a fixed number of observations are drawn successively in time. An adaptive two-stage procedure is proposed for this testing problem. The first stage is based on order statistics and the second stage is based on rank test statistics. The empirical powers of the adaptive test are compared with some rank tests through Monte Carlo simulation. The results show that the adaptive test is suitable over a wide class of underlying distributions.