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Title: Frechet change point detection for random objects Authors:  Hans-Georg Mueller - University of California Davis (United States)
Paromita Dubey - Stanford University (United States) [presenting]
Abstract: Change-point detection is a challenging problem when the underlying data space is a metric space where one does not have basic algebraic operations like the addition of the data points and the scalar multiplication. We propose a method to infer the presence and location of change points in the distribution of a sequence of independent data taking values in a general metric space. Change points are viewed as locations at which the distribution of the data sequence changes abruptly in terms of either its Frechet mean or Frechet variance or both. The proposed method is based on comparisons of Frechet variances before and after putative change-point locations. First, we will establish that under the null hypothesis of no change-point, the limit distribution of the proposed scan function is the square of a standardized Brownian Bridge. Next, we will show that when a change point exists, (1) the proposed test is consistent under contiguous alternatives and (2) the estimated location of the change-point is consistent. We will illustrate the efficacy of the proposed approach in empirical studies and real data applications with sequences of maternal fertility distributions.