Abstract

In this talk, we consider an estimation problem in a tensor regression model with multiple change-points. Under a dependence structure of the error and covariates that is as weak as an L2-mixingale array, we establish the asymptotic properties of the unrestricted tensor estimator (UE) and restricted tensor estimator (RE). Moreover, we propose a class of shrinkage estimators (SEs) in the case of tensor regression, and we derive sufficient conditions for the SEs to dominate the UE. In addition, we consider an inference problem in the model for the special case of a possible change-point. Specifically, we consider a general hypothesis testing problem on a tensor parameter and the studied testing problem includes as a special case testing the absence of a change-point. To this end, we derive a test for testing the restriction and its asymptotic power and we prove that the proposed test is consistent. Finally, we present some simulation and real data results that corroborate the theoretical results.