Related papers: Statistical tests based on R\'{e}nyi entropy estim…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they…
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…
We consider the Student-t and Student-r distributions, which maximise Renyi entropy under a covariance condition. We show that they have information-theoretic properties which mirror those of the Gaussian distributions, which maximise…
Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the…
Two new goodness of fit tests for the Pareto type-I distribution for complete and right censored data are proposed using fixed point characterization based on Steins type identity. The asymptotic distributions of the test statistics under…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
Characteristic-function based goodness-of-fit tests are suggested for multivariate observations. The test statistics, which are straightforward to compute, are defined as two-sample criteria measuring discrepancy between multivariate ranks…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…