Related papers: Order statistics on the spacings between order sta…
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…
Opial's inequality and its ramifications play an important role in the theory of differential and difference equations. A sharp unifying generalization of Opial's inequality is presented that contains both its continuous and discrete…
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…
Let $T$ be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for $T$ are obtained. The bounds are the best possible for many known statistics.…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Dispersive order is a type of variability order for comparing the variability in probability distributions. Star order compares the skewness of probability distributions. This work considers dispersive and star orders of extreme order…
For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…
A new notion is introduced of matrix order indices which relate the matrix norm and its trace. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well…
We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Given a suitable arithmetic function h, we investigate the average order of h as it ranges over the values taken by an integral binary form F. A general upper bound is obtained for this quantity, in which the dependence upon the…
This thesis details a class of partial orders on the space of probability distributions and the space of density operators which capture the idea of information content. Some links to domain theory and computational linguistics are also…
We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium.…
Given a permutation statistic $s : S_n \to \mathbb{R}$, define the mean statistic $\bar{s}$ as the statistic which computes the mean of $s$ over conjugacy classes. We describe a way to calculate the expected value of $s$ on a product of $t$…
In our previous publication [Kogan et al, Phys. Rev. {\bf 48}, 9404 (1993)] we considered the issue of statistics of radiation diffusively propagating in a disordered medium. The consideration was in the framework of diagrammatic techniques…
A definition for the statistical significance by constructing a correlation between the normal distribution integral probability and the p-value observed in an experiment is proposed, which is suitable for both counting experiment and…