Related papers: Multiplier U-processes: sharp bounds and applicati…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
Artifact-centric business process models have gained increasing momentum recently due to their ability to combine structural (i.e., data related) with dynamical (i.e., process related) aspects. In particular, two main lines of research have…
We establish a multivariate empirical process central limit theorem for stationary $\R^d$-valued stochastic processes $(X_i)_{i\geq 1}$ under very weak conditions concerning the dependence structure of the process. As an application we can…
This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We characterize the statistical bootstrap for the estimation of information-theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately,…
Diagnostic accuracy studies assess sensitivity and specificity of a new index test in relation to an established comparator or the reference standard. The development and selection of the index test is usually assumed to be conducted prior…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…
In this work, we use the theory of error bounds to study metric regularity of the sum of two multifunctions, as well as some important properties of variational systems. We use an approach based on the metric regularity of epigraphical…
Bootstrap is a useful tool for making statistical inference, but it may provide erroneous results under complex survey sampling. Most studies about bootstrap-based inference are developed under simple random sampling and stratified random…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
Multilevel or hierarchical data structures can occur in many areas of research, including economics, psychology, sociology, agriculture, medicine, and public health. Over the last 25 years, there has been increasing interest in developing…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
Continuation refers to the operation by which the cumulative distribution function of a discontinuous random vector is made continuous through multilinear interpolation. The copula that results from the application of this technique to the…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
The main purpose of this paper is to investigate the strong approximation of the $p$-fold integrated empirical process, $p$ being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of…
In this paper, we study the asymptotic distribution of some U-statistics whose entries are functions of empirical moments computed from non-overlapping consecutive blocks of an underlying weakly dependent process. The length of these blocks…