Andrii Babii, Eric Ghysels, Junsu Pan
arXiv 26 Dec 2022 · Econometrics · publishedJournal of Econometrics (2025) · 1 citations (OpenAlex)
arXiv:2212.12981 · PDF · DOI · OpenAlex · Extracted main text
Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes the $d$-dimensional panel as a sum of a reduced rank component and an idiosyncratic noise, generalizing traditional factor models for two-dimensional panels. We consider a tensor factor model corresponding to the notion of a reduced multilinear rank of a tensor. We show that for a strong factor model, a simple tensor principal component analysis algorithm is optimal for estimating factors and loadings. When the factors are weak, the convergence rate of simple TPCA can be improved with alternating least-squares iterations. We also provide inferential results for factors and loadings and propose the first test to select the number of factors. The new tools are applied to the problem of imputing missing values in a multidimensional panel of firm characteristics.
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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 | F. L. Hitchcock (1927) The expression of a tensor or a polyadic as a sum of products | 0.928 | 4 | 3 | 100% |
| 2 | S. Bryzgalova, S. Lerner, M. Lettau, and M. Pelger (2024) Missing financial data | 0.883 | 16 | 3 | 69% |
| 3 | L. R. Tucker (1966) Some mathematical notes on three-mode factor analysis | 0.843 | 3 | 3 | 100% |
| 4 | A. Zhang and D. Xia (2018) Tensor SVD: Statistical and computational limits | 0.737 | 3 | 2 | 100% |
| 5 | N. El Karoui (2003) On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n tend to infinity | 0.644 | 3 | 2 | 67% |
| 6 | J. Bai (2003) Inferential theory for factor models of large dimensions | 0.644 | 2 | 2 | 100% |
| 7 | J. Bai and S. Ng (2023) Approximate factor models with weaker loadings | 0.644 | 2 | 2 | 100% |
| 8 | J. D. Carroll and J.-J. Chang (1970) Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition | 0.644 | 2 | 2 | 100% |
| 9 | R. Chen, D. Yang, and C.-H. Zhang (2022) Factor models for high-dimensional tensor time series | 0.644 | 2 | 2 | 100% |
| 10 | Y. Han, R. Chen, D. Yang, and C.-H. Zhang (2025) Tensor factor model estimation by iterative projection | 0.644 | 2 | 2 | 100% |
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