Related papers: Concentration for independent random variables wit…
We provide an inequality which is a useful tool in studying both large deviation results and limit theorems for sums of random fields with "negligible" small values. In particular, the inequality covers cases of stable limits for random…
We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
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…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
(This is the third version of a working paper.) We develop a family of self-normalized concentration inequalities for marginal mean under martingale-difference structure and $\phi/\tilde{\phi}$-mixing conditions, where the latter includes…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the ``intrinsic''…
We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials
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…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
We establish Hoeffding-type concentration inequalities for the low and high tail bounds of sums of exchangeable random variables. Our results exhibit an anti-symmetry in such tail bounds due to the assumption of exchangeability, a…
We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…
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 paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…
A statistical description of heavy particles suspended in incompressible rough self-similar flows is developed. It is shown that, differently from smooth flows, particles do not form fractal clusters. They rather distribute inhomogeneously…