SUMMARY Non-parametric techniques are introduced for the change-point problem. Exact and approximate results are obtained for testing the null hypothesis of no change. The methods are illustrated by the analysis of three sets of data illustrating the techniques for zero-one observations, Binomial observations and continuous observations. Some comparisons are made with methods based on CUSUMS.

A Non-parametric Approach to the Change-point Problem

General guidance is offered as to the methodology of change detection in time series of hydrological data, embracing stages such as preparing a suitable data set, exploratory analysis, application of adequate statistical tests and interpretation of results. Although the paper cannot go into full details of the many existing tests, it gives an easy-to-follow overview, offering practical hints and describing caveats and misconceptions. It serves as a refresher, raising attention to essential things that have often been ignored. A particular recommendation of the paper is that greater use of distribution-free testing methods, particularly resampling methods, should be made. These methods are recommended because they are particularly suited to hydrological data, which are often strongly skewed (non-normal), seasonal and serially correlated. Resampling techniques are flexible, robust and powerful, and require only minimal assumptions to be made about the data.

https://rmgsc.cr.usgs.gov/outgoing/threshold_articles/Kundzewica_Robson2004.pdf

Change detection in hydrological records— a review of the methodology

https://www.tandfonline.com/doi/pdf/10.1623/hysj.49.1.7.53993

Change detection in hydrological records—a review of the methodology / Revue méthodologique de la détection de changements dans les chroniques hydrologiques

The literature on nonparametric or distribution-free control charts for univariate variables data is examined. The advantages of these charts have over more traditional distribution-based control charts are demonstrated. Constructive criticism of the li..

Nonparametric Control Charts: An Overview and Some Results

SUMMARY 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.

A simple cumulative sum type statistic for the change-point problem with zero-one observations

A cumulative sum technique which allows distribution-free tests is developed and applied to the problem of detecting a change in median of a rainfall distribution.

C. A. McGilchrist

Papers

Note on a Distribution-free CUSUM Technique