Related papers: On the Bennett-Hoeffding inequality
A Berry-Esseen bound is obtained for self-normalized martingales under the assumption of finite moments. The bound coincides with the classical Berry-Esseen bound for standardized martingales. An example is given to show the optimality of…
In this paper, we obtain new bounds for the inequalities of Simpson and Hermite-Hadamard type for functions whose second derivatives absolute values are P-convex. These bounds can be much better than some obtained bounds. Some applications…
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 improve the rate function of McDiarmid's inequality for Hamming distance. In particular, applying our result to the separately Lipschitz functions of independent random variables, we also refine the convergence rate function of…
In a Hilbert space setting H, for convex optimization, we analyze the fast convergence properties as t tends to infinity of the trajectories generated by a third-order in time evolution system. The function f to minimize is supposed to be…
We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…
We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\lambda$ is at most $e^{-\lambda^2 / (R^q Var(f))}$ for sufficiently small $\lambda$, where $R$ is an absolute constant.…
A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions…
The Hanson-Wright inequality is an upper bound for tails of real quadratic forms in independent random variables. In this work, we extend the Hanson-Wright inequality for the Ky Fan k-norm for the polynomial function of the quadratic sum of…
The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
We consider the problem of estimating small ball probabilities $\mathbb P\{f(G) \leqslant \delta \mathbb Ef(G)\}$ for sub-additive,positively homogeneous functions $f$ with respect to the Gaussian measure. We establish estimates that depend…
In this short note we derive, for bounded domains, an upper bound for a Friedrichs type constant in a weighted Friedrichs type inequality. This upper bound generalizes a well known upper bound of the Friedrichs constant. This upper bound is…
We consider the regular model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad et. al. We derive an upper bound on the satisfiability threshold and NAE-satisfiability threshold for regular random $k$-SAT for any…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
We derive new comparison inequalities between weak and strong moments of norms of random vectors with optimal (up to an universal factor) constants. We discuss applications to the concentration of log-concave random vectors and bounds on…
This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…