Identification of distributional heterogeneity under maximum adjacent separation subspace

This study develops a novel dimension reduction strategy to enhance distributional change point detection, which addresses the curse of dimensionality for some popular nonparametric change point detection methods. Firstly, based on the squared Hellinger distance, we propose the maximum adjacent separation subspace (MASS), which preserves the integrity of the change point information. Recognizing the challenge of identifying precise change point locations beforehand, we further present an exhaustive estimator of MASS based on a segmentation method. This estimator retains key change point information after dimension reduction and eliminates the need to identify exact change point locations. Additionally, we present its asymptotic property. Finally, we obtain the estimator by using the Riemannian Manifold Optimization method and apply a classical nonparametric change point detection to the lower dimensional data. Through several simulations and applications to real data, we demonstrate that the dimension reduction strategy enhances the performance of nonparametric change point detection methods in finite sample scenarios.