Related papers: \'Equidistribution et diff\'erentiabilit\'e
An axiomatics for indistinguishability of elementary particles in terms of hidden variables is presented in a manner which depart from the standard approaches usually given to hidden variables. Quantum distribution functions are also…
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite…
In this Note we introduce a new methodology for Bayesian inference through the use of $\phi$-divergences and the duality technique. The asymptotic laws of the estimates are established.
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…
We study the fair allocation problem of indivisible items with subsidy. In this paper, we focus on the notion of fairness - equitability (EQ), which requires that items be allocated such that all agents value the bundle they receive…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
The basic idea of voting protocols is that nodes query a sample of other nodes and adjust their own opinion throughout several rounds based on the proportion of the sampled opinions. In the classic model, it is assumed that all nodes have…
The Gini index signals only the dispersion of the distribution and is not very sensitive to income differences at the tails of the distribution. The widely used index of inequality can be adjusted to also measure distributional asymmetry by…
E-variables are a relatively new approach for testing statistical hypotheses that has been experiencing major development during the last several years. In this paper we introduce the method of e-variable-approximability and use it to…
Developing classification methods with high accuracy that also avoid unfair treatment of different groups has become increasingly important for data-driven decision making in social applications. Many existing methods enforce fairness…
Several resource allocation settings involve agents with unequal entitlements represented by weights. We analyze weighted fair division from an asymptotic perspective: if $m$ items are divided among $n$ agents whose utilities are…
Elicitability is a property of $\mathbb{R}^k$-valued functionals defined on a set of distribution functions. These functionals represent statistical properties of a distribution, for instance its mean, variance, or median. They are called…
We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss.…
We address the problem of uncertainty quantification for graph-structured data, or, more specifically, the problem to quantify the predictive uncertainty in (semi-supervised) node classification. Key questions in this regard concern the…
We study the empirical measure of the output of the t-distributed stochastic neighbour embedding algorithm when the initial data is given by n independent, identically distributed inputs. We prove that under certain assumptions on the…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.