相关论文: Stability of Cramer's Characterization of Normal L…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
A statistical framework is introduced for a broad class of problems involving synchronization or registration of data across a sensor network in the presence of noise. This framework enables an estimation-theoretic approach to the design…
The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.
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…
The Cramer-Rao product of the Fisher information and the variance of a probability density \rho(x), defined on a domain \Delta \in R^D, is found to have a minimum value reached by the density associated with the ground state of the harmonic…
Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.
Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…
A statistical algorithm for estimating the characteristic parameter $\alpha$ of the stable law is presented and the estimate of its quadratic deviation is obtained in the paper. This algorithm is applied in the description of the…
Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
The variance and the entropy power of a continuous random variable are bounded from below by the reciprocal of its Fisher information through the Cram\'{e}r-Rao bound and the Stam's inequality respectively. In this note, we introduce the…
When the distribution of a random (N) sum of independent copies of a r.v X is of the same type as that of X we say that X is N-sum stable. In this paper we consider a generalization of stability of geometric sums by studying distributions…
Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic,…
The electronic local density of states of solids, if normalized correctly, represents the probability density that the electron at a specific position has a particular energy. Because this probability density can vary in space in disordered…
In this paper, we present three remarkable properties of the normal distribution: first that if two independent variables's sum is normally distributed, then each random variable follows a normal distribution (which is referred to as the…
For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting…
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…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…