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.

翻译：张量在神经影像学、数据挖掘、数字营销等领域具有广泛的应用。CANDECOMP/PARAFAC（CP）张量分解能有效减少参数数量以实现降维，因此在张量回归中发挥着关键作用。然而，CP分解中存在秩选择的不确定性问题。本文提出了一种模型平均方法，通过对不同秩的候选张量回归模型的估计量进行加权，以处理这种不确定性。当所有候选模型均被错误设定时，我们证明了该模型平均估计量具有渐近最优性。当候选模型中包含正确模型时，我们证明了参数的一致性以及模型平均权重的收敛性。仿真与实证研究表明，所提方法优于竞争方法，并具有广阔的应用前景。