Related papers: Sharp bounds for cumulative distribution functions
We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to $U$-statistics satisfying the weak assumption of decomposability in the Hoeffding…
We study the arithmetic (real) function, with f 'essentially bounded'. In particular, we obtain non-trivial bounds, through f 'correlations', for the 'Selberg integral' and the 'symmetry integral' of f in almost all short intervals…
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical…
The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…
We give an overview of published algorithms by our group and of current activities and future plans. In particular, we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we…
We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…
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…
The cumulative distribution function of the non-central chi-square distribution $\chi_\nu'^2(\lambda),\, \nu\in\mathbb{R}^+$ possesses an integral representation in terms of a generalized Marcum $Q$-function. Regarding some already known…
Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
Let $\mathbf{B}_n=\mathbf {S}_n(\mathbf {S}_n+\alpha_n\mathbf {T}_N)^{-1}$, where $\mathbf {S}_n$ and $\mathbf {T}_N$ are two independent sample covariance matrices with dimension $p$ and sample sizes $n$ and $N$, respectively. This is the…
Simple upper and lower bounds are established for the integral $\int_0^x\mathrm{e}^{-\beta u}u^\nu t_{\mu,\nu}(u)\,\mathrm{d}u$, where $x>0$, $0<\beta<1$, $\mu+\nu>-2$, $\mu-\nu\geq-3$, and $t_{\mu,\nu}(x)$ is the modified Lommel function…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…
We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total variation. As a by-product, we answer some open questions…
We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…
A \emph{double extrema form} of the calculus of variations is put forward in which only the smallest one of the finite differences is physically meaningful to represent the variational derivatives defined on the discrete points. The most…
Concentration inequalities are widely used for analyzing machine learning algorithms. However, current concentration inequalities cannot be applied to some of the most popular deep neural networks, notably in natural language processing.…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…