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Tensor PCA for Factor Models

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

Abstract

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.

Citation extraction

76
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1F. L. Hitchcock (1927) The expression of a tensor or a polyadic as a sum of products0.92843100%
2S. Bryzgalova, S. Lerner, M. Lettau, and M. Pelger (2024) Missing financial data0.88316369%
3L. R. Tucker (1966) Some mathematical notes on three-mode factor analysis0.84333100%
4A. Zhang and D. Xia (2018) Tensor SVD: Statistical and computational limits0.73732100%
5N. El Karoui (2003) On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n tend to infinity0.6443267%
6J. Bai (2003) Inferential theory for factor models of large dimensions0.64422100%
7J. Bai and S. Ng (2023) Approximate factor models with weaker loadings0.64422100%
8J. D. Carroll and J.-J. Chang (1970) Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition0.64422100%
9R. Chen, D. Yang, and C.-H. Zhang (2022) Factor models for high-dimensional tensor time series0.64422100%
10Y. Han, R. Chen, D. Yang, and C.-H. Zhang (2025) Tensor factor model estimation by iterative projection0.64422100%

Showing the top 10 of 76 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Factor-Augmented Machine Learning Panel Regressions0.51121
2Firm Heterogeneity and Macroeconomic Fluctuations: a Functional VAR model0.40511
3Modewise Additive Factor Model for Matrix Time Series0.40511
4Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flows0.40511