Related papers: On the Impact of Approximation Errors on Extreme Q…

In many applications, random fields reflect uncertain parameters, and often their moments are part of the modeling process and thus well known. However, there are practical situations where this is simply not the case. Therefore, we do not…

In recent years, tensors have been applied to different applications in science and engineering fields. In order to establish theory about tail bounds of the tensors summation behavior, this work extends previous work by considering the…

We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…

Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…

In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…

We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…

In this paper, we introduce a new approximation of the cumulative distribution function of the standard normal distribution based on Tocher's approximation. Also, we assess the quality of the new approximation using two criteria namely the…

An expression is proposed for determining the error caused on entropy estimates by finite sample effects. This expression is based on the Ansatz that the ranked distribution of probabilities tends to follow an empirical Zipf law.

This article is a review of functional $f(R)$ approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This…

Most of the literature on the solution of linear ill-posed operator equations, or their discretization, focuses only on the infinite-dimensional setting or only on the solution of the algebraic linear system of equations obtained by…

Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications - e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme…

Let $\{Z(\tau,s), (\tau,s)\in [a,b]\times[0,T]\}$ with some positive constants $a,b,T$ be a centered Gaussian random field with variance function $\sigma^{2}(\tau,s)$ satisfying $\sigma^{2}(\tau,s)=\sigma^{2}(\tau)$. We firstly derive the…

So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…

Let $X_{1},X_{2},...$ be a sequence of independent copies (s.i.c) of a real random variable (r.v.) $X\geq 1$, with distribution function $df$ $F(x)=\mathbb{P}% (X\leq x)$ and let $X_{1,n}\leq X_{2,n} \leq ... \leq X_{n,n}$ be the order…

The central limit theorem introduced by Stute [The central limit theorem under random censorship. Ann. Statist. 1995; 23: 422-439] does not hold for some class of heavy-tailed distributions. In this paper, we make use of the extreme value…

Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as…

This paper investigates the impact of distributional uncertainty on key risk measures under the partial knowledge of underlying distributions characterized by their first two moments and shape information (specifically symmetry and/or…

Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…

The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…

Chernoff bounds are a powerful application of the Markov inequality to produce strong bounds on the tails of probability distributions. They are often used to bound the tail probabilities of sums of Poisson trials, or in regression to…