Elynn Chen, Yuefeng Han, Jiayu Li, Ke Xu
arXiv 31 Dec 2025 · Statistics — Methodology
arXiv:2512.25025 · PDF · DOI · OpenAlex · Extracted main text
We introduce a Modewise Additive Factor Model (MAFM) for matrix-valued time series that captures row-specific and column-specific latent effects through an additive structure, offering greater flexibility than multiplicative frameworks such as Tucker and CP factor models. In MAFM, each observation decomposes into a row-factor component, a column-factor component, and noise, allowing distinct sources of variation along different modes to be modeled separately. We develop a computationally efficient two-stage estimation procedure: Modewise Inner-product Eigendecomposition (MINE) for initialization, followed by Complement-Projected Alternating Subspace Estimation (COMPAS) for iterative refinement. The key methodological innovation is that orthogonal complement projections completely eliminate cross-modal interference when estimating each loading space. We establish convergence rates for the estimated factor loading matrices under proper conditions. We further derive asymptotic distributions for the loading matrix estimators and develop consistent covariance estimators, yielding a data-driven inference framework that enables confidence interval construction and hypothesis testing. As a technical contribution of independent interest, we establish matrix Bernstein inequalities for quadratic forms of dependent matrix time series. Numerical experiments on synthetic and real data demonstrate the advantages of the proposed method over existing approaches.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Han, Yuefeng and Chen, Rong and Yang, Dan and Zhang, Cun-Hui (2024) Tensor factor model estimation by iterative projection self | 1.000 | 12 | 4 | 100% |
| 2 | Bai, J (2003) Inferential theory for factor models of large dimensions | 1.000 | 10 | 3 | 100% |
| 3 | Han, Yuefeng and Yang, Dan and Zhang, Cun-Hui and Chen, Rong (2024) CP factor model for dynamic tensors self | 1.000 | 6 | 3 | 100% |
| 4 | Chen, Bin and Han, Yuefeng and Yu, Qiyang (2026) Estimation and inference for CP tensor factor models self | 1.000 | 5 | 3 | 100% |
| 5 | Yuan, Chaofeng and Gao, Zhigen and He, Xuming and Huang, Wei and Guo… (2023) Two-way dynamic factor models for high-dimensional matrix-valued time series | 0.928 | 4 | 4 | 100% |
| 6 | Chen, Elynn and Fan, Jianqing (2023) Statistical inference for high-dimensional matrix-variate factor models self | 0.874 | 7 | 2 | 100% |
| 7 | Chang, Jinyuan and He, Jing and Yang, Lin and Yao, Qiwei (2023) Modelling matrix time series via a tensor CP-decomposition | 0.737 | 3 | 2 | 100% |
| 8 | Rong Chen and Dan Yang and Cun-Hui Zhang (2022) Factor Models for High-Dimensional Tensor Time Series | 0.737 | 3 | 2 | 100% |
| 9 | Lam, Clifford and Yao, Qiwei (2012) Factor Modeling for High-Dimensional Time Series: Inference for the Number of Factors | 0.737 | 3 | 2 | 100% |
| 10 | Yu, Long and He, Yong and Kong, Xinbing and Zhang, Xinsheng (2022) Projected estimation for large-dimensional matrix factor models | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 44 scored citations.