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.

Changepoint problem, continguity, Gaussian processes, U-statistics, weak convergence, weight functions, Wiener process
dx.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