Reviving pseudo-inverses: Asymptotic properties of large dimensional Moore-Penrose and Ridge-type inverses with applications
复兴伪逆:大维Moore-Penrose与岭型逆的渐近性质及应用
In this paper, we derive high-dimensional asymptotic properties of the Moore-Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic behavior of the weighted sample trace moments of generalized inverse matrices are deduced in terms of the partial exponential Bell polynomials which can be easily computed in practice. The existent results for pseudo-inverses are extended in…