Related papers: One-Sided Confidence About Functionals Over Tangen…

Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

Uniformly valid inference for cointegrated vector autoregressive processes has so far proven difficult due to certain discontinuities arising in the asymptotic distribution of the least squares estimator. We extend asymptotic results from…

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…

This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…

The aim of this paper is to study a wide class of non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i.e., functions of not necessarily bounded variation admitting…

In many applications, the parameter of interest involves a simplex-valued weight which is identified as a solution to an optimization problem. Examples include synthetic control methods with group-level weights and various methods of model…

We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal…

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.

Image analysis frequently deals with shape estimation and image reconstruction. The ob jects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a…

Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…

The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…

We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of…

We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a forward invariant Siegel disk is unbounded if and only if it contains at least one asymptotic value on the boundary. Our argument is…

We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are the notions of amenable cones and facial residual…

In this paper we prove generic results concerning Hardy spaces in one or several complex variables. More precisely, we show that the generic function in certain Hardy type spaces is totally unbounded and hence non-extentable, despite the…

Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting…

Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…

We study the problems of testing and learning high-dimensional discrete convex sets. The simplest high-dimensional discrete domain where convexity is a non-trivial property is the ternary hypercube, $\{-1,0,1\}^n$. The goal of this work is…