Related papers: Efficient and Stable Multi-Dimensional Kolmogorov-…
We are interested in the estimation of the distance in total variation $$ \Delta := \|P_{f(X)} - P_{g(X)}\|_{\mathrm var} $$ between distributions of random variables $f(X)$ and $g(X)$ in terms of proximity of $f$ and $g.$ We propose a…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…
The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence one obtains an invariance principle for such polynomials. This generalizes known results concerning the total…
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
Recent findings by Jahn, T. Ullrich, Voigtlaender [10] relate non-linear sampling numbers for the square norm to quantities involving trigonometric best $m-$term approximation errors in the uniform norm. Here we establish new results for…
Discrepancy measures between probability distributions are at the core of statistical inference and machine learning. In many applications, distributions of interest are supported on different spaces, and yet a meaningful correspondence…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces $({\mathbb X}, d, \mu_1)$ and $({\mathbb X}, d, \mu_2)$, we are interested in the problem of determining from finite data…
Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in high-dimensional statistics and machine learning, as…
A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of…
We show how to improve the discrepancy of an iid sample by moving only a few points. Specifically, modifying \( O(m) \) sample points on average reduces the Kolmogorov-Smirnov distance to the population distribution to \(1/m\).
For rescaled additive functionals of the sine-process, upper bounds are obtained for their speed of convergence to the Gaussian distribution with respect to the Kolmogorov-Smirnov metric. Under scaling with coefficient $R$ the…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…
The Kolmogorov-Smirnov (KS) test is a nonparametric statistical test used to test for differences between univariate probability distributions. The versatility of the KS test has made it a cornerstone of statistical analysis across many…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…