B0871
Title: Reviving pseudo-inverses: asymptotic properties of large dimensional generalized inverses with applications
Authors: Nestor Parolya - Delft University of Technology (Netherlands) [presenting]
Taras Bodnar - Stockholm University (Sweden)
Abstract: High-dimensional asymptotic properties of the Moore-Penrose inverse and the ridge-type inverse of the sample covariance matrix are derived. In particular, the analytical expressions of the weighted sample trace moments are deduced for both generalized inverse matrices and are present by using the partial exponential Bell polynomials which can easily be computed in practice. The existent results are extended in several directions: (i) First, the population covariance matrix is not assumed to be a multiplier of the identity matrix; (ii) Second, the assumption of normality is not used in the derivation; (iii) Third, the asymptotic results are derived under the high-dimensional asymptotic regime. The findings are used in the construction of improved shrinkage estimators of the precision matrix that minimizes the Frobenius norm. Also, shrinkage estimators of the coefficients of the high-dimensional regression model and the weights of the global minimum variance portfolio are obtained. Finally, the finite sample properties of the derived theoretical results are investigated via an extensive simulation study.
