Convergence in distribution of multiple change point estimators

In this paper we establish the asymptotic distribution for a class of multiple change point estimators in the following setup: a finite sequence of independent random variables consists of segments given by a known number of so-called change points such that the underlying distribution differs from segment to segment. In a nonparametric framework the proposed estimator is defined as the maximizing point of weighted multivariate U-statistic processes. We show that the proposed estimators converge in distribution to a maximizer of a sum of random walks with drift.