相关论文: Stein's method, Palm theory and Poisson process ap…

Let $(X,d)$ be a locally compact separable ultrametric space. Given a measure $m$ on $X$ and a function $C$ defined on the set $\mathcal{B}$ of all balls $B\subset X$ we consider the hierarchical Laplacian $L=L_{C}$. The operator $L$ acts…

For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the…

This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the…

There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…

Rough path theory provides one with the notion of signature, a graded family of tensors which characterise, up to a negligible equivalence class, and ordered stream of vector-valued data. In the last few years, use of the signature has…

We use Stein's method to provide non asymptotic $L^1$ bounds to the normal for functionals of associated point processes. As for supporting tools, we use the connection between association and $\alpha$-mixing properties that was recently…

Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…

Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…

This document presents the statistical methods used to process low-level measurements in the presence of noise. These methods can be classical or Bayesian. The question is placed in the general framework of the problem of nuisance…

We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…

We use Stein's method to obtain a bound on the distance between scaled $p$-dimensional random walks and a $p$-dimensional (correlated) Brownian Motion. We consider dependence schemes including those in which the summands in scaled sums are…

We consider the normal approximation of Kabanov-Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only difference operators of the integrand of the Kabanov-Skorohod…

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…

Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…

The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…

By a method inspired of the Stein's method, we derive an upper-bound of the Rubinstein distance between two absolutely continuous probability measures on configurations space. As an application, we show that the best way to approximate a…

Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also…

A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and…

The central limit theorem is one of the most fundamental results in probability and has been successfully extended to locally dependent data and strongly-mixing random fields. In this paper, we establish its rate of convergence for…