Some Results on Estimating a Change-Point Using Non-Parametric Statistics

摘要

A general class of statistics, derived from a Mann-Whitney-Wilcoxon two sample statistic, for estimating the change point in a sequence of random variables is considered. These statistics should perform well when the underlying populations are not normal but are long-tailed. Some asymptotic results are discussed and comparisons of a simple non-change point are made. Some Monte Carlo results are also reported to give some indication of small sample behavior. The nonparametric statistic performs well under the assumption of long-tailed distributions.