Title: Shrinkage estimators in tensor regression with change-points
Authors: Severien Nkurunziza - University of Windsor (Canada)
Mai Ghannam - University of Windsor (Canada) [presenting]
Abstract: An estimation problem about the tensor coefficient in a tensor regression model with multiple and unknown number of change-points is considered. We generalize some recent findings in five ways. First, the problem studied is more general than the one in the context of a matrix parameter with multiple change-points. Second, we develop asymptotic results of the tensor estimators in the tensor regression model with unknown change-points. Third, we construct a class of shrinkage tensor estimators that encloses the unrestricted estimator (UE) and the restricted estimator (RE). Fourth, we generalize some identities, which are crucial in studying the risk dominance of tensor estimators. Fifth, we show that the proposed shrinkage estimators perform better than the UE. The additional novelty of the established results is that the dependence structure of the errors is as weak as that of $L_2$-mixingale tensors.