Related papers: Poisson approximation with applications to stochas…
In circular plot sampling, trees within a given distance from the sample plot location constitute a sample, which is used to infer characteristics of interest for the forest area. If the sample is collected using a technical device located…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric $\bar{d}_1$ that combines…
Subordinators are infinitely divisible distributions on the positive half-line. They are often used as mixing distributions in Poisson mixtures. We show that appropriately scaled Poisson mixtures can approximate the mixing subordinator and…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…
The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its…
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic…
We provide a general theorem bounding the error in the approximation of a random measure of interest--for example, the empirical population measure of types in a Wright-Fisher model--and a Dirichlet process, which is a measure having…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
This paper introduces some new characterizations of COM-Poisson random variables. First, it extends Moran-Chatterji characterization and generalizes Rao-Rubin characterization of Poisson distribution to COM-Poisson distribution. Then, it…
We consider the contour representation of the infinite volume Ising model at low temperature. Fix a subset V of Z^d, and a (large) N such that calling G_{N,V} the set of contours of length at least N intersecting V, there are in average one…
Fix a subset $S \subset \mathbb{R}^n$ of volume at most $c n$ that satisfies $S \cap (-S) = \emptyset$. We consider two point processes in $S$: the first is the Poisson point process of intensity one, and the second is the restriction of a…
Let $X$ be a $d$-dimensional random vector and $X_\theta$ its projection onto the span of a set of orthonormal vectors $\{\theta_1,...,\theta_k\}$. Conditions on the distribution of $X$ are given such that if $\theta$ is chosen according to…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…