Related papers: A Note on New Bernstein-type Inequalities for the …

We establish weighted Bernstein inequalities in $L^p$ space for the doubling weight on the conic surface $\mathbb{V}_0^{d+1} = \{(x,t): \|x\| = t, x \in \mathbb{R}^d, t\in [0,1]\}$ as well as on the solid cone bounded by the conic surface…

We consider the problem of estimating a parameter associated to a Bayesian inverse problem. Treating the unknown initial condition as a nuisance parameter, typically one must resort to a numerical approximation of gradient of the…

We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.

In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter $1\leq r\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative…

Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data are proposed. This results in not…

While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…

Instrumental variable methods allow for inference about the treatment effect by controlling for unmeasured confounding in randomized experiments with noncompliance. However, many studies do not consider the observed compliance behavior in…

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…

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…

Using the renewal approach we prove Bernstein-like inequalities for additive functionals of geometrically ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The coefficient in the…

We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in…

Two types of Bernstein inequalities are established on the unit ball in $\mathbb{R}^d$, which are stronger than those known in the literature. The first type consists of inequalities in $L^p$ norm for a fully symmetric doubling weight on…

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of log-concave measures on the half-line in terms of log-concavity of the…

We establish Bernstein's inequalities for functions of general (general-state-space and possibly non-reversible) Markov chains. These inequalities achieve sharp variance proxies and encompass the classical Bernstein inequality for…

In this paper, we propose a new approach for deriving probabilistic inequalities. Our main idea is to exploit the information of underlying distributions by virtue of the monotone likelihood ratio property and Berry-Essen inequality.…

In this paper, we show that the likelihood-ratio measure (a) is invariant with respect to dominating sigma-finite measures, (b) satisfies logical consequences which are not satisfied by standard $p$-values, (c) respects frequentist…

We describe some recent approaches to likelihood based inference in the presence of nuisance parameters. Our approach is based on plotting the likelihood function and the $p$-value function, using recently developed third order…

We present a new PAC-Bayesian generalization bound. Standard bounds contain a $\sqrt{L_n \cdot \KL/n}$ complexity term which dominates unless $L_n$, the empirical error of the learning algorithm's randomized predictions, vanishes. We manage…

We study the local limit theorem for weighted sums of Bernoulli variables. We show on examples that this is an important question in the general theory of the local limit theorem, and which turns up to be not well explored. The examples we…