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Hölder norm test statistics for epidemic change. (English) Zbl 1084.62083

Summary: To detect epidemic change in the mean of a sample of size n, we introduce new test statistics UI and DI based on weighted increments of partial sums. We obtain their limit distributions under the null hypothesis of no change in the mean. Under alternative hypothesis our statistics can detect very short epidemics of length \(\log^\gamma n\), \(\gamma>1\). Using self-normalization and adaptiveness to modify UI and DI, allows us to prove the same results under very relaxed moment assumptions. Trimmed versions of UI and DI are also studied.

MSC:

62M07 Non-Markovian processes: hypothesis testing
62E20 Asymptotic distribution theory in statistics
60F17 Functional limit theorems; invariance principles
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