Related papers: Moderate deviations in Poisson approximation: a fi…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
We consider the first serial correlation coefficient under an AR(1) model where errors are not assumed to be Gaussian. In this case it is necessary to consider bootstrap approximations for tests based on the statistic since the distribution…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
In this paper, we develop Stein's method for binomial approximation using the stop-loss metric that allows one to obtain a bound on the error term between the expectation of call functions. We obtain the results for a locally dependent…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
In this paper, we derive the moderate deviation principle for stationary sequences of bounded random variables with values in a Hilbert space. The conditions obtained are expressed in terms of martingale-type conditions. The main tools are…
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…
In this work we consider the primal mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is non-standard as the line source causes the solutions to be singular. We start by…
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…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
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…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates…
Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…
We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we…