Related papers: Fisher information and the central limit theorem
In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…
A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included…
An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.
Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as a suitable supremum. In addition, we enforce equivariance by a…
We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincare inequalities, to provide a better understanding of the…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
Using a representation of the score function by means of the divergence operator we exhibit a sufficient condition, in terms of the negative moments of the norm of the Malliavin derivative, under which convergence in Fisher information to…
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy…
In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support…
Basic general properties are considered for the Fisher-type information involving higher order derivatives. They are used to explore various properties of probability densities and to derive Stam-type inequalities.
We consider the behaviour of the Fisher information of scaled sums of independent and identically distributed random variables in the Central Limit Theorem regime. We show how this behaviour can be related to the second-largest non-trivial…
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
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…