Projected estimation for large-dimensional matrix factor models

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