Related papers: Sharp Empirical Bernstein Bounds for the Variance …
Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…
New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…
We use the generic chaining device proposed by Talagrand to establish exponential bounds on the deviation probability of some suprema of random processes. Then, given a random vector $\xi$ in $\R^{n}$ the components of which are independent…
We establish a Berry--Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best possible for many known statistics. As applications,…
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
For an ergodic Brownian diffusion with invariant measure $\nu$, we consider a sequence of empirical distributions ($\nu$n) n$\ge$1 associated with an approximation scheme with decreasing time step ($\gamma$n) n$\ge$1 along an adapted…
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the…
Given a weakly dependent stationary process, we describe the transition between a Berry-Esseen bound and a second order Edgeworth expansion in terms of the Berry-Esseen characteristic. This characteristic is sharp: We show that Edgeworth…
We prove a multivariate version of Bernstein's inequality about the probability that degenerate $U$-statistics take a value larger than some number $u$. This is an improvement of former estimates for the same problem which yields an…
Bounding causal effects analytically, rather than numerically, is appealing for its interpretability and conceptual clarity. Existing sharp methods rely on optimization-based approaches such as the Balke-Pearl framework, whose computational…
Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…
\noindent We study the asymptotic behavior of a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables. We prove a Berry-Esseen bound…
This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \(\xiv\) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The…
We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremisers in log-concave settings when the moments of summands are…