Related papers: Modified Bernstein's inequality for sums of indepe…
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 study the exact constants in the moment inequalities for sums of centered independent random variables: improve their asymptotics, low and upper bounds, calculate more exact asymptotics, elaborate the numerical algorithm for their…
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…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
In this paper we obtain a Bernstein type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix…
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
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…
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…
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…
We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.
In this paper we give new deviation inequalities of Bernstein's type for the partial sums of weakly dependent time series. The loss from the independent case is studied carefully. We give non mixing examples such that dynamical systems and…
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…
Large deviation inequalities for ergodic sums is an important subject since the seminal contribution of Bernstein for independent random variables with finite variances, followed by the Chernoff method and the Hoefding result for…
In this article, we provide an extension of the Chen-Stein inequality for Poisson approximation in the total variation distance for sums of independent Bernoulli random variables in two ways. We prove that we can improve the rate of…
We study how well moments of sums of independent symmetric random variables with logarithmically concave tails may be approximated by moments of Gaussian random variables.
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…
We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…
In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…