Some results on estimating a change-point using non-parametric type statistics

A Mann-Whitney type statistic is used to estimate a change-point when a change, at an unknown point in a sequence of random variables, has taken place. This estimate is compared, using Monte Carlo techniques, with the normal theory maximum likelihood estimate, when a location change has occurred, for different underlying distributions ranging from the normal to the long tailed “normal over uniform” distribution. The distribution of the Mann-Whitney type estimate remains fairly constant over the various distributions. Two generalisations of the statistic are considered and investigated.