Related papers: On the Fisher information matrix for multivariate …
The main aim of this paper is to extend the semiparametric inference methodology, recently investigated for Real Elliptically Symmetric (RES) distributions, to Complex Elliptically Symmetric (CES) distributions. The generalization to the…
This paper is mainly dedicated to an extension of the Slepian-Bangs formula to non-circular complex elliptical symmetric (NC-CES) distributions, which is derived from a new stochastic representation theorem. This formula includes the…
This letter aims at deriving a Semiparametric Slepian-Bangs (SSB) formula for Complex Elliptically Symmetric (CES) distributed data vectors. The Semiparametric Cram\'{e}r-Rao Bound (SCRB), related to the proposed SSB formula, provides a…
The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…
The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…
A new family of distributions indexed by the class of matrix variate contoured elliptically distribution is proposed as an extension of some bimatrix variate distributions. The termed \emph{multimatrix variate distributions} open new…
The Fisher information matrix (FIM) has long been of interest in statistics and other areas. It is widely used to measure the amount of information and calculate the lower bound for the variance for maximum likelihood estimation (MLE). In…
The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…
This chapter presents a short overview of real elliptically symmetric (RES) distributions, complemented by circular complex elliptically symmetric (C-CES) and noncircular CES (NC-CES) distributions as complex representations of RES…
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…
In this paper, we analyze the impact of compressed sensing with complex random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal…
By using the $q$-Gaussian distribution derived by the maximum entropy method for spatially-correlated $N$-unit nonextensive systems, we have calculated the generalized Fisher information matrix of $g_{\theta_n \theta_m}$ for $(\theta_1,…
The eigenvalues and eigenvectors of the Fisher information matrix (FIM) can reveal the most and least sensitive directions of a system and it has wide application across science and engineering. We present a symplectic variant of the…
There is a need for new models for characterizing dependence in multivariate data. The multivariate Gaussian distribution is routinely used, but cannot characterize nonlinear relationships in the data. Most non-linear extensions tend to be…
The goal of this work is to introduce and investigate a generalised Fisher Information in the setting of linear Fokker-Planck equations. This functional, which depends on two functions instead of one, exhibits the same decay behaviour as…
When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as…
We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…
This short note reviews so-called Natural Gradient Descent (NGD) for multivariate Gaussians. The Fisher Information Matrix (FIM) is derived for several different parameterizations of Gaussians. Careful attention is paid to the symmetric…
This paper proposes an efficient numerical integration formula to compute the normalizing constant of Fisher--Bingham distributions. This formula uses a numerical integration formula with the continuous Euler transform to a Fourier-type…
In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on…