  Tensors have broad applications in neuroimaging, data mining, digital
marketing, etc. CANDECOMP/PARAFAC (CP) tensor decomposition can effectively
reduce the number of parameters to gain dimensionality-reduction and thus plays
a key role in tensor regression. However, in CP decomposition, there is
uncertainty which rank to use. In this article, we develop a model averaging
method to handle this uncertainty by weighting the estimators from candidate
tensor regression models with different ranks. When all candidate models are
misspecified, we prove that the model averaging estimator is asymptotically
optimal. When correct models are included in the candidate models, we prove the
consistency of parameters and the convergence of the model averaging weight.
Simulations and empirical studies illustrate that the proposed method has
superiority over the competition methods and has promising applications.
