In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously established in [6] is given. Further, along with generalized De-Bruijn's identity, we provide new interpretation of the concavity for the entropy power.

The Fisher information matrix determines how much information a measurement brings about the parameters that index the underlying probability distribution for the measurement. In this paper we assume that the parameters structure the mean value vector in a multivariate normal distribution. The Fisher matrix is. then a Gramian constructed from the sensitivity vectors that characterize the first-...

Consider a Bayesian optimal design with many support points which poses the problem of collecting data with a few number of observations at each design point. Under such a scenario the asymptotic property of using Fisher information matrix for approximating the covariance matrix of posterior ML estimators might be doubtful. We suggest to use Bhattcharyya matrix in deriving the information matri...

In this paper we derive some properties of the Bezout matrix and relate the Fisher information matrix for a stationary ARMA process to the Bezoutian. Some properties are explained via realizations in state space form of the derivatives of the white noise process with respect to the parameters. A factorization of the Fisher information matrix as a product in factors which involve the Bezout matr...