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Tensor Factor Model Estimation by Iterative Projection

Yuefeng Han, Rong Chen, Dan Yang, Cun-Hui Zhang

arXiv 4 Jun 2020 · Statistics — Methodology · publishedThe Annals of Statistics (2024) · 14 citations (OpenAlex)

arXiv:2006.02611 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal projections of the original tensor time series. These approaches extend the existing estimation procedures and improve the estimation accuracy and convergence rate significantly as proven in our theoretical investigation. Our algorithms are similar to the higher order orthogonal projection method for tensor decomposition, but with significant differences due to the need to unfold tensors in the iterations and the use of autocorrelation. Consequently, our analysis is significantly different from the existing ones. Computational and statistical lower bounds are derived to prove the optimality of the sample size requirement and convergence rate for the proposed methods. Simulation study is conducted to further illustrate the statistical properties of these estimators.

Citation extraction

64
references
130
in-text mentions
64
distinct cited
10
self-citations
17,447
main-text words

appendix boundary found by appendix_command · 48% of the source is main text. Read the extracted text to check this.

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
1barticle[author] Lam, CliffordC. Yao, QiweiQ (2012) )1.00053100%
2barticle[author] Wang, DongD., Liu, XialuX. Chen, RongR (2019) ) self1.00053100%
3barticle[author] Zhang, AnruA. Xia, DongD (2018) )0.9568388%
4barticle[author] Wedin, Per-keP.- (1972) )0.9416383%
5barticle[author] Chen, RongR., Yang, DanD. Zhang, Cun-HuiC.-H (2022) a) self0.90916675%
6barticle[author] Lam, CliffordC., Yao, QiweiQ. Bathia, NeilN (2011) )0.81142100%
7barticle[author] Ma, ZongmingZ. Wu, YihongY (2015) )0.7636267%
8barticle[author] Chen, RongR., Yang, DanD. Zhang, Cun-HuiC.-H (2022) b) self0.7373367%
9barticle[author] Bai, JushanJ (2003) )0.73732100%
10barticle[author] Stock, James H.J. H. Watson, Mark W.M. W (2002) )0.73732100%

Showing the top 10 of 64 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
1Modewise Additive Factor Model for Matrix Time Series1.000124
2CP Factor Model for Dynamic Tensors0.977156
3Dynamic Matrix Factor Models for High Dimensional Time Series0.909125
4Estimation and Inference for CP Tensor Factor Models0.84333
5Identification and Estimation for Matrix Time Series CP-factor Models0.64422
6Panel Coupled Matrix-Tensor Clustering Model with Applications to Asset Pricing0.64422
7Simultaneous Decorrelation of Matrix Time Series0.40511
8Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models0.40511
9Diffusion Index Forecasting with Tensor Data0.40511
10Threshold Tensor Factor Model in CP Form0.40511