Let X1, X2,... be independent random variables. We study asymptotic behaviour of two-time parameter empirical type processes based on observations, ranks and sequential ranks. We introduce weight functions and derive the limiting distributions of these processes under the null hypothesis of Xi being identically distributed, as well as under a class of continguous alternatives which can accommodate the possible occurrence of a changepoint in the series of measurements.

empirical processes, p4 changepoint problem, p4 contiguity, p4 Gaussian processes, p4 invariance principles, p4 Le Cam's lemmas, p4 likelihood ratio, p4 ranks, p4 sequential ranks, p4 weight functions
dx.doi.org/10.1016/0304-4149(94)90125-2
Stochastic Processes and their Applications
School of Mathematics and Statistics

Szyszkowicz, B. (1994). Weak convergence of weighted empirical type processes under contiguous and changepoint alternatives. Stochastic Processes and their Applications, 50(2), 281–313. doi:10.1016/0304-4149(94)90125-2