Nonparametric adaptive change point estimation and on line detection

Under standard conditions of change point problems with one or both distributions being unknown, we propose efficient on line and off line nonparametric algorithms for detecting and estimating the change point. They are based on histogram density estimators, which allows applications involving ordinal and categorical data. Also, they are designed to detect any changes in distribution, not necessarily related to the location or scale parameters. EfFiciency of the proposed schemes is demonstrated by relevant inequalities for the mean delay and the mean time between false alarms. Asymptotically, they are shown to behave similarly to the most efficient procedures based on the known distributions. The stopping rule achieves an asymptotically linear rnean delay and an exponential mean time between false alarms. The guidelines on selecting the threshold and the partition for the histogram density estimation are given, based on the obtained results. Proposed methods are applied to the England temperatures data and the Vostok ice core record to detect the global climate changes