Wasserstein information matrix (Q6170229)

Information matrices for statistical models, similar to the classical Fisher information matrices, are studied by means of the \(L^2\)-Wasserstein metric. New Wasserstein score functions are introduced to this end and covariance operators are investigated in statistical models, delivering, in particular, Wasserstein-Cramer-Rao bounds for estimations. Online asymptotic efficiency for the Wasserstein natural gradient and a Poincaré efficiency for the Wasserstein natural gradient of maximal likelihood estimation are then established. Some analytical examples of such matrices are provided, too.