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 about 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 set of 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Publication:

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION2025, VOL. 120, NO. 550, 1115–1126: Theory and Methods

https://doi.org/10.1080/01621459.2024.2398164

Author:

Qiushi Bu

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

University of Chinese Academy of Sciences, Beijing, China

Hua Liang

Department of Statistics, George Washington University, Washington, DC

Xinyu Zhang

International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, China

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Jiahui Zou

School of Statistics, Capital University of Economics and Business, Beijing, China