Related papers: Empirical estimation of entropy functionals with c…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…
We first investigate on the asymptotics of the Kolmogorov metric entropy and nonlinear n-widths of approximation spaces on some function classes on manifolds and quasi-metric measure spaces. Secondly, we develop constructive algorithms to…
Recent theoretical developments revived the interest in charged particle multiplicities and their wide-spread parametrization, the negative binomial distribution (NBD). The central observable of the studies is the Shannon entropy of the…
kNN based ensemble methods minimise the effect of outliers by identifying a set of data points in the given feature space that are nearest to an unseen observation in order to predict its response by using majority voting. The ordinary…
We calculate the quantum Renyi entropy in a phase space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
This paper studies the problem of estimating the differential entropy $h(S+Z)$, where $S$ and $Z$ are independent $d$-dimensional random variables with $Z\sim\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$. The distribution of $S$ is unknown, but $n$…
We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved…
Expected values weighted by the inverse of a multivariate density or, equivalently, Lebesgue integrals of regression functions with multivariate regressors occur in various areas of applications, including estimating average treatment…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
Simulation-based inference (SBI) with neural posterior estimation (NPE) provides rapid X-ray spectral fitting in both Gaussian and Poisson regimes by learning approximate parameter posteriors from simulations. We investigate auto-encoders…
Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…
Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…
When using the K-nearest neighbors method, one often ignores uncertainty in the choice of K. To account for such uncertainty, Holmes and Adams (2002) proposed a Bayesian framework for K-nearest neighbors (KNN). Their Bayesian KNN (BKNN)…
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…
Asymptotic properties of three estimators of probability density function of sample maximum $f_{(m)}:=mfF^{m-1}$ are derived, where $m$ is a function of sample size $n$. One of the estimators is the parametrically fitted by the…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
Empirical best prediction (EBP) is a well-known method for producing reliable proportion estimates when the primary data source provides only small or no sample from finite populations. There are potential challenges in implementing…
R\'enyi divergences play a pivotal role in information theory, statistics, and machine learning. While several estimators of these divergences have been proposed in the literature with their consistency properties established and minimax…