Related papers: \'Equidistribution et diff\'erentiabilit\'e

We propose alternative discriminant measures for selecting the best basis among a large collection of orthonormal bases for classification purposes. A generalization of the Local Discriminant Basis Algorithm of Saito and Coifman is…

We formulate an abstract notion of equidistribution for families of $\lambda$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $\sigma$-moment generating functions…

We study a wide class of metrics in a Lebesgue space with a standard measure, the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the…

We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized…

In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting,…

We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…

Predicting potential outcomes of interventions from observational data is crucial for decision-making in medicine, but the task is challenging due to the fundamental problem of causal inference. Existing methods are largely limited to point…

A variant of Phragm\'en's method for proportional representation via approval voting is briefly explored. Instead of D'Hondt's rule, this variant generalizes Sainte-Lagu\"e's rule.

Equivariant diffusion policies (EDPs) combine the generative expressivity of diffusion models with the strong generalization and sample efficiency afforded by geometric symmetries. While steering these policies with reinforcement learning…

Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…

We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…

This paper derives a novel representation of the exponential discounting model that allows one to assess departures from the model via a measure of efficiency. The approach uses a revealed preference methodology that does not make any…

We consider concepts and models for measuring inequality in the distribution of resources with a focus on how inequality varies as a function of covariates. Lorenz introduced a device for measuring inequality in the distribution of income…

We prove a new equidistribution estimate for the divisor function in arithmetic progression to moduli that have two small factors. We give two applications. First, we show an asymptotic formula for the divisor function over arithmetic…

Let K be a global field of characteristic not 2. Let Z be a symmetric variety defined over K and S a finite set of places of K. We obtain counting and equidistribution results for the S-integral points of Z. Our results are effective when K…

Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

In this paper, a new method of detection of election fraud is proposed. This method is based on the calculation of the ratio of two standard normal random variables; estimation of parameters of obtained sample and comparison of these…

For analysis of a high-dimensional dataset, a common approach is to test a null hypothesis of statistical independence on all variable pairs using a non-parametric measure of dependence. However, because this approach attempts to identify…