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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Keywords Changepoint problem, continguity, Gaussian processes, U-statistics, weak convergence, weight functions, Wiener process
Persistent URL dx.doi.org/10.1016/0167-7152(91)90039-T
Journal Statistics and Probability Letters
Szyszkowicz, B. (1991). Changepoint problems and contiguous alternatives. Statistics and Probability Letters, 11(4), 299–308. doi:10.1016/0167-7152(91)90039-T