Related papers: Multivariate Ranks and Quantiles using Optimal Tra…
A multivariate one-sample location test based on the center-outward ranks and signs is considered, and two different testing procedures are proposed for centrally symmetric distributions. The first test is based on a random division of the…
Quantum metric, a probe to spacetime of the Hilbert space, has been found measurable in the nonlinear electronic transport thus has attracted tremendous interest. However, without comparing with mechanisms tied to disorder, it is still…
In this article, we propose a novel characterization of law-invariant and coherent risk measures, based on a generalized optimal transport problem in which the second marginal of the admissible plans is not fixed, but required to lie within…
Nonparametric tests provide robust and powerful alternatives to the corresponding least squares methods. There are two approaches to nonparametric pairwise comparisons of treatment effects, the method based on pairwise rankings and the…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We prove that Kendall's Rank correlation matrix converges to the Mar\v{c}enko-Pastur law, under the assumption that the observations are i.i.d random vectors $X_1$, $\dots$, $X_n$ with components that are independent and absolutely…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
In many life science experiments or medical studies, subjects are repeatedly observed and measurements are collected in factorial designs with multivariate data. The analysis of such multivariate data is typically based on multivariate…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to…
We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic bounds with explicit constants, that hold with high probabilities. We…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use…
Recently, optimal transport-based approaches have gained attention for deriving counterfactuals, e.g., to quantify algorithmic discrimination. However, in the general multivariate setting, these methods are often opaque and difficult to…