Weak convergence of weighted empirical type processes under contiguous and changepoint alternatives

Abstract

Let X 1, X 2,… 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 X i 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.