Related papers: A Statistical Distance Derived From The Kolmogorov…
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each…
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…
Properties of random mixed states of order $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure, the trace distance between two random states…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…
The Davis--Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between…
In terms of the Dirac representation of sample mean and the weak convergence of empirical distributions that holds almost surely, we construct a new proof for a strong law of large numbers of Kolmogorov's type with i.i.d. random variables…
Quantifying the similarity of two or more datasets has widespread applications in statistics and machine learning. The method choice is, however, difficult due to the abundance of proposed methods and the lack of neutral comparison studies,…
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for…
A new method for the determination of electric signal time-shifts is introduced. As the Kolmogorov-Smirnov test, it is based on the comparison of the cumulative distribution functions of the reference signal with the test signal. This…
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…
The cumulative distribution and quantile functions for the one-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDF appears straight…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
In this work we propose a methodology for assessment of pedestrian models continuous in space. With respect to the Kolmogorov-Smirnov distance between two data clouds, representing for instance simulated and the corresponding empirical…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
We study statistical inference on the similarity/distance between two time-series under uncertain environment by considering a statistical hypothesis test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The sampling…
We propose a robust methodology to evaluate the performance and computational efficiency of non-parametric two-sample tests, specifically designed for high-dimensional generative models in scientific applications such as in particle…
A novel method for computing exact p-values of one-sided statistics from the Kolmogorov-Smirnov family is presented. It covers the Higher Criticism statistic, one-sided weighted Kolmogorov-Smirnov statistics, and the one-sided Berk-Jones…