Projected estimation for large-dimensional matrix factor models

Yu, Lei; He, Yong; Kong, Xin-Bing; Zhang, Xinsheng

doi:10.1016/j.jeconom.2021.04.001

Cited by 36 publications

(83 citation statements)

References 22 publications

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“…Wang et al (2019) propose estimators of the factor loading matrices and of numbers of the row and column factors based on the eigen-analysis of the auto-cross-covariance matrix, under the assumption that the idiosyncratic term E t is white noise. Chen and Fan (2021) propose an α-PCA method for inference of (1.1), which conducts eigen-analysis of a weighted average of the sample mean and the column (row) sample covariance matrix; Yu et al (2021) proposed a projected estimation method which further improved the estimation efficiency of the factor loading matrices and the numbers of factors. He et al (2021) proposed a strong rule to determine whether there is a factor structure of matrix time series and also propose a sequential procedure to determine the numbers of factors.…”

Section: Introductionmentioning

confidence: 99%

“…In the current work, we first propose least squares estimators for the matrix factor models. The most interesting finding is that the least squares estimators are equivalent to the projected estimators by Yu et al (2021), i.e., the projected estimators minimizes the least squares loss function. This finding provides another rationale for the projected estimation procedure by Yu et al (2021), which is initially proposed for reducing the magnitudes of the idiosyncratic error components and thereby increasing the signal-to-noise ratio.…”

Section: Introductionmentioning

confidence: 99%

“…The most interesting finding is that the least squares estimators are equivalent to the projected estimators by Yu et al (2021), i.e., the projected estimators minimizes the least squares loss function. This finding provides another rationale for the projected estimation procedure by Yu et al (2021), which is initially proposed for reducing the magnitudes of the idiosyncratic error components and thereby increasing the signal-to-noise ratio. Motivated by the least squares formulation, we further propose a robust method for estimating largedimensional matrix factor model, by substituting the least squares loss function with the Huber Loss function.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

“…The resultant estimators turns out to be equivalent to the corresponding projected estimators in Yu et al (2021), which enjoys the nice properties of reducing the magnitudes of the idiosyncratic error components and thereby increasing the signal-to-noise ratio. We derive the convergence rate of the theoretical minimizers under sub-Gaussian tails, instead of the one-step iteration estimators by Yu et al (2021). Motivated by the least squares formulation, we further consider a robust method for estimating large-dimensional matrix factor model by utilizing Huber Loss function.…”

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confidence: 99%

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Matrix Factor Analysis: From Least Squares to Iterative Projection

He¹,

Kong²,

Liu³

et al. 2021

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In the article we focus on large-dimensional matrix factor models and propose estimators of factor loading matrices and factor score matrix from the perspective of minimizing least squares objective function. The resultant estimators turns out to be equivalent to the corresponding projected estimators in Yu et al. (2021), which enjoys the nice properties of reducing the magnitudes of the idiosyncratic error components and thereby increasing the signal-to-noise ratio. We derive the convergence rate of the theoretical minimizers under sub-Gaussian tails, instead of the one-step iteration estimators by Yu et al. (2021). Motivated by the least squares formulation, we further consider a robust method for estimating large-dimensional matrix factor model by utilizing Huber Loss function. Theoretically, we derive the convergence rates of the robust estimators of the factor loading matrices under finite fourth moment conditions. We also propose an iterative procedure to estimate the pair of row and column factor numbers robustly. We conduct extensive numerical studies to investigate the empirical performance of the proposed robust methods relative to the sate-of-theart ones, which show the proposed ones perform robustly and much better than the existing ones when data are heavy-tailed while perform almost the same (comparably) with the projected estimators when data are light-tailed, and as a result can be used as a safe replacement of the existing ones. An application to a Fama-French financial portfolios dataset illustrates its empirical usefulness.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Matrix Factor Analysis: From Least Squares to Iterative Projection

He¹,

Kong²,

Liu³

et al. 2021

Preprint

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Low‐rank latent matrix‐factor prediction modeling for generalized high‐dimensional matrix‐variate regression

Zhang

et al. 2023

Statistics in Medicine

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Motivated by diagnosing the COVID‐19 disease using two‐dimensional (2D) image biomarkers from computed tomography (CT) scans, we propose a novel latent matrix‐factor regression model to predict responses that may come from an exponential distribution family, where covariates include high‐dimensional matrix‐variate biomarkers. A latent generalized matrix regression (LaGMaR) is formulated, where the latent predictor is a low‐dimensional matrix factor score extracted from the low‐rank signal of the matrix variate through a cutting‐edge matrix factor model. Unlike the general spirit of penalizing vectorization plus the necessity of tuning parameters in the literature, instead, our prediction modeling in LaGMaR conducts dimension reduction that respects the geometric characteristic of intrinsic 2D structure of the matrix covariate and thus avoids iteration. This greatly relieves the computation burden, and meanwhile maintains structural information so that the latent matrix factor feature can perfectly replace the intractable matrix‐variate owing to high‐dimensionality. The estimation procedure of LaGMaR is subtly derived by transforming the bilinear form matrix factor model onto a high‐dimensional vector factor model, so that the method of principle components can be applied. We establish bilinear‐form consistency of the estimated matrix coefficient of the latent predictor and consistency of prediction. The proposed approach can be implemented conveniently. Through simulation experiments, the prediction capability of LaGMaR is shown to outperform some existing penalized methods under diverse scenarios of generalized matrix regressions. Through the application to a real COVID‐19 dataset, the proposed approach is shown to predict efficiently the COVID‐19.

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