Xin-Bing Kong, Yong-Xin Liu, Long Yu, Peng Zhao
arXiv 18 Aug 2022 · Statistics — Methodology · 3 citations (OpenAlex)
arXiv:2208.08693 · PDF · DOI · OpenAlex · Extracted main text
This paper introduces a matrix quantile factor model for matrix-valued data with low-rank structure. We estimate the row and column factor spaces via minimizing the empirical check loss function with orthogonal rotation constraints. We show that the estimates converge at rate $(\min{p_1p_2,p_2T,p_1T})^{-1/2}$ in the average Frobenius norm, where $p_1$, $p_2$ and $T$ are the row dimensionality, column dimensionality and length of the matrix sequence, respectively. This rate is faster than that of the quantile estimates via “flattening" the matrix model into a large vector model. To derive the central limit theorem, we introduce a novel augmented Lagrangian function, which is equivalent to the original constrained empirical check loss minimization problem. Via the equivalence, we prove that the Hessian matrix of the augmented Lagrangian function is locally positive definite, resulting in a locally convex penalized loss function around the true factors and their loadings. This easily leads to a feasible second-order expansion of the score function and readily established central limit theorems of the smoothed estimates of the loadings. We provide three consistent criteria to determine the pair of row and column factor numbers. Extensive simulation studies and an empirical study justify our theory.
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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 | Chen, L., J. J. Dolado, and J. Gonzalo (2021) Quantile factor models | 1.000 | 14 | 5 | 100% |
| 2 | Yu, L., Y. He, X. Kong, and X. Zhang (2022) Projected estimation for large-dimensional matrix factor models self | 1.000 | 6 | 3 | 100% |
| 3 | Wang, D., X. Liu, and R. Chen (2019) Factor models for matrix-valued high-dimensional time series | 0.874 | 5 | 2 | 100% |
| 4 | Bai, J. and S. Ng (2002) Determining the number of factors in approximate factor models | 0.644 | 2 | 2 | 100% |
| 5 | Chen, E. Y. and J. Fan (2023) Statistical inference for high-dimensional matrix-variate factor models | 0.511 | 2 | 1 | 100% |
| 6 | Ahn, S. C. and A. R. Horenstein (2013) Eigenvalue ratio test for the number of factors | 0.405 | 1 | 1 | 100% |
| 7 | Ando, T. and J. Bai (2021) Quantile co-movement in financial markets: A panel quantile model with unobserved heterogeneity | 0.405 | 1 | 1 | 100% |
| 8 | Barigozzi, M. and L. Trapani (2020) Sequential testing for structural stability in approximate factor models | 0.405 | 1 | 1 | 100% |
| 9 | Chang, J., J. He, L. Yang, and Q. Yao (2023) Modelling matrix time series via a tensor CP-decomposition | 0.405 | 1 | 1 | 100% |
| 10 | Ge, R., C. Jin, and Y. Zheng (2017) No spurious local minima in nonconvex low rank problems: A unified geometric analysis | 0.405 | 1 | 1 | 100% |
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