Nonparametric Change-Point Problems and Optimal Nested Plans

AbstractWe consider nonparametric methods for detecting a change-point in the distribution of a sequence of observations based on using nested plans. Using nonparametric tests for the inner test statistic, we develop nested plans providing fast detection of a change. Moreover, the methodology allows the computation of exact (non-asymptotic) expressions for the mean and for the standard deviation of the run length for the in-control time to false alarm. Special attention is given to finding optimal nonparametric nested plans.