Related papers: Concentration bounds for sampling without replacem…
Let $T$ be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for $T$ are obtained. The bounds are the best possible for many known statistics.…
We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained…
Concentration bounds for non-product, non-Haar measures are fairly recent: the first such result was obtained for contracting Markov chains by Marton in 1996 via the coupling method. The work that followed, with few exceptions, also used…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
The asymptotic behaviour of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessarily compact) and connected Riemannian manifolds with…
We perform the apriori analysis of solutions to critical nonlinear elliptic equations on manifolds with boundary. The solutions are of minimizing type. The originality is that we impose no condition on the boundary, which leads us to assume…
Ferguson's Dirichlet process plays an important role in nonparametric Bayesian inference. Let $P_a$ be the Dirichlet process in $\mathbb{R}$ with a base probability measure $H$ and a concentration parameter $a>0.$ In this paper, we show…
We present a tail inequality for suprema of empirical processes generated by variables with finite $\psi_\alpha$ norms and apply it to some geometrically ergodic Markov chains to derive similar estimates for empirical processes of such…
This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform H\"older continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
For an indeterminate Hamburger moment problem we consider an infinite family of analytic densities solving the moment problem and we prove that they all have finite (Shannon) entropy. These densities are either all bounded or all unbounded.…
The Heisenberg limit provides a fundamental bound on the achievable estimation precision with a limited number of $N$ resources used (e.g., atoms, photons, etc.). Using entangled quantum states makes it possible to scale the precision with…
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…
Polyak-Ruppert averaging is a widely used technique to achieve the optimal asymptotic variance of stochastic approximation (SA) algorithms, yet its high-probability performance guarantees remain underexplored in general settings. In this…
This paper is mainly concerned with the existence of extremals for the Adams inequality. We first establish an upper bound for the classical Adams functional along of all concentrated sequences in $W^{m,\frac{n}{m}}_{\mathcal{N}}(\Omega)$,…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…
We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…
We consider the convergence of empirical processes indexed by functions that depend on an estimated parameter $\eta$ and give several alternative conditions under which the ``estimated parameter'' $\eta_n$ can be replaced by its natural…
We prove several different anti-concentration inequalities for functions of independent Bernoulli-distributed random variables. First, motivated by a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn, we prove some "Poisson-type"…