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Title: Abrupt change in mean avoiding variance estimation without boundary value problem and block bootstrap Authors:  Barbora Pestova - The Czech Academy of Sciences, Institute of Computer Science (Czech Republic) [presenting]
Abstract: Sequences of weakly dependent observations that are naturally ordered in time are considered. Their constant mean is possibly subject to change at most once at some unknown time point. The aim is to test whether such an unknown change has occurred or not. The change point methods presented here rely on ratio type statistics based on maxima of cumulative sums. These detection procedures for the abrupt change in mean are also robustified by considering a general score function. The main advantage of the proposed approach is that the variance of the observations neither has to be known nor estimated. The asymptotic distribution of the test statistic under the no change null hypothesis is derived and is free of any tuning parameters. Moreover, we prove the consistency of the test under the alternative. A block bootstrap method is developed in order to improve computational performance of the asymptotic methods. The validity of the bootstrap algorithm is shown. The results are illustrated through a simulation study.