We study the problem of multiple change-point estimation in the mean in the high-dimensional setting, where the vector of mean changes could be either sparse or non-sparse, and where the additive noise could be heterogeneous and potentially dependent.
A three?stage procedure is proposed. First, we test whether there exist any change-points in a given interval via wild bootstrap on the lagged sample auto-covariance matrix. Second, we obtain a projection direction for that interval if change-points are suspected in that interval. Finally, we apply an existing univariate change-point estimation algorithm, such as narrowest-over-threshold method or wild binary segmentation to the projected series.
We provide theoretical results of our procedure on both the number of estimated change-points and the convergence rates of their locations. We also demonstrate its competitive empirical performance in our numerical experiments for a wide range of data generating mechanisms.