# Projected Estimation for Large-dimensional Matrix Factor Models

arXiv: https://arxiv.org/abs/2003.10285 · HTML: https://mlsanity.com/paper/2003.10285/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Tucker Diffusion Model for High-dimensional Tensor Generation](https://mlsanity.com/paper/2604.00481/) (2026)
- [Strongly Consistent Community Detection in Popularity Adjusted Block Models](https://mlsanity.com/paper/2506.07224/) (2025)

## Abstract (arXiv)

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that for a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative procedure is given to specify the pair of row and column factor numbers. Extensive numerical studies verify the empirical performance of the projection method. Two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincides with financial, economic, or geographical interpretations.