We consider U-statistic type processes which can be used for detecting a changepoint in a random sequence. The asymptotic results when all random variables are assumed to have the same distribution are already known. We derive the limiting distribution of such processes under contiguous alternatives.

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doi.org/10.1016/0167-7152(91)90039-T
Statistics and Probability Letters
School of Mathematics and Statistics

Szyszkowicz, B. (1991). Changepoint problems and contiguous alternatives. Statistics and Probability Letters, 11(4), 299–308. doi:10.1016/0167-7152(91)90039-T