A0830
Title: An adaptive-to-change ridge-ratio criterion for multiple change points in high-dimensional tensors
Authors: Jiaqi Huang - Beijing Normal University (China) [presenting]
Junhui Wang - Chinese University of Hong Kong (Hong Kong)
Lixing Zhu - Beijing Normal University (China)
Abstract: Two criteria are proposed for detecting change structure in tensor data, which include vector and matrix as order-one and two tensors. The first criterion is based on the Euclidean norm of the moving sums of tensor data, the second is based on the Euclidean norm of the moving sums of slices. To handle both dense and sparse scenarios, the norms defined are signal-adaptive to screen out those non-signal elements. Two signal statistics are respectively the ratios and the minimum of ratios of two moving sums in consecutive segments with a data-driven ridge function. The latter is going to take care of the scenarios where a fiber could have a very high dimension. The estimation consistency of the number of changes and their locations is derived. The results can still hold when the dimensions of fibers and the number of changes diverge at certain rates. Numerical studies are conducted to examine the finite sample performances of the proposed method and compare it with some existing competitors. We also analyse two real data examples for illustration.
