We show that the maximally selected standardized U-statistic goes in distribution to an infinite sum of weighted chi-square random variables in the degenerate case. The result is applied to the detection of possible changes in the distribution of a sequence observation.
"Limit theorem for maximum of standardized U-statistics with an application." Ann. Statist. 24 (5) 2266 - 2279, October 1996. https://doi.org/10.1214/aos/1069362321