A Simple Cumulative Sum Type Statistic for the Change-Point Problem with Zero-One Observations

A simple cumulative sum type statistic for the change-point with zero-one observations is introduced. A conditional test of no change against change is introduced and compared with a likelihood ratio test. The estimation of the change-point is also considered, using the simple statistic, and the method is shown to be asymptotically equivalent to the maximum likelihood estimator in certain circumstances and almost equivalent in others. To investigate the small sample behaviour, simulation experiments were carried out and these showed the new estimator to be generally superior to the maximum likelihood estimator.