Some nonparametric methods for changepoint problems

Abstract

A general model for changepoint problems is discussed from a nonparametric viewpoint. The test statistics introduced are based on Cramér-von Mises functionals of certain processes and are shown to converge in distribution to corresponding Gaussian functionals (under the assumption of no change in distribution, H0). We also demonstrate how the distribution of the limiting Gaussian functionals may be tabulated. Finally, properties of the tests under the alternative hypothesis of exactly one changepoint occurring are studied, and some examples are given.

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