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Gaussian Multiplicative Chaos (GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is Gaussian field on $\mathbb R^d$ (or an open subset of it) whose correlation function is of the form $ K(x,y)= \log…

Probability · Mathematics 2020-12-23 Hubert Lacoin

Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Pek\"oz, R\"ollin, and Ross (2016, arXiv:1309.4183 [math.PR]) exploited characterizing distributional fixed…

Probability · Mathematics 2022-08-08 Tobias Johnson , Erol Peköz

Mutual information is a measure of the dependence between random variables that has been used successfully in myriad applications in many fields. Generalized mutual information measures that go beyond classical Shannon mutual information…

Information Theory · Computer Science 2021-07-30 Kevin R. Moon , Kumar Sricharan , Alfred O. Hero

We present a novel method for testing the hypothesis of equality of two correlation matrices using paired high-dimensional datasets. We consider test statistics based on the average of squares, maximum and sum of exceedances of Fisher…

Methodology · Statistics 2018-04-10 Adria Caballe , Natalia Bochkina , Claus Mayer , Ioannis Papastathopoulos

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

Discrete Mathematics · Computer Science 2015-03-12 Elisângela Silva Dias , Diane Castonguay , Mitre Costa Dourado

In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real $(\beta = 1)$, complex ($\beta = 2)$ and real…

Probability · Mathematics 2015-06-16 Peter J. Forrester

This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the…

Functional Analysis · Mathematics 2022-01-03 Hongyu He

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…

Statistics Theory · Mathematics 2013-12-09 Johanna Hardin , Stephan Ramon Garcia , David Golan

Measuring the degree of inequality expressed by a multivariate statistical distribution is a challenging problem, which appears in many fields of science and engineering. In this paper, we propose to extend the well known univariate Gini…

Statistics Theory · Mathematics 2024-09-17 Gennaro Auricchio , Paolo Giudici , Giuseppe Toscani

We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…

Machine Learning · Computer Science 2024-10-24 Diego Marcondes , Ulisses Braga-Neto

An occurrence of a classical pattern p in a permutation \pi is a subsequence of \pi whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be…

Combinatorics · Mathematics 2008-05-31 Einar Steingrimsson

In order to encode additional statistical information in data fusion and transfer learning applications, we introduce a generalized covariance constraint for the matching component analysis (MCA) transfer learning technique. We provide a…

Machine Learning · Computer Science 2022-12-15 Nick Lorenzo , Sean O'Rourke , Theresa Scarnati

Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…

Statistics Theory · Mathematics 2022-05-31 Edgar Dobriban

We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite…

Statistics Theory · Mathematics 2014-06-10 Andrius Čiginas , Dalius Pumputis

Generalised regression estimation allows one to make use of available auxiliary information in survey sampling. We develop three types of generalised regression estimator when the auxiliary data cannot be matched perfectly to the sample…

Methodology · Statistics 2020-05-20 Li-Chun Zhang

We develop some theoretical results for a robust similarity measure named "generalized min-max" (GMM). This similarity has direct applications in machine learning as a positive definite kernel and can be efficiently computed via…

Methodology · Statistics 2016-08-02 Ping Li , Cun-Hui Zhang

Consider a discrete locally finite subset $\Gamma$ of $R^d$ and the complete graph $(\Gamma,E)$, with vertices $\Gamma$ and edges $E$. We consider Gibbs measures on the set of sub-graphs with vertices $\Gamma$ and edges $E'\subset E$. The…

Probability · Mathematics 2010-09-17 Pablo A. Ferrari , Eugene A. Pechersky , Valentin V. Sisko , Anatoly A. Yambartsev

Gravitational wave observations of quasicircular compact binary mergers in principle provide an arbitrarily complex likelihood over eight independent intrinsic parameters: the masses and spins of the two merging objects. In this work, we…

General Relativity and Quantum Cosmology · Physics 2022-01-05 Vera Delfavero , Richard O'Shaughnessy , Daniel Wysocki , Anjali Yelikar

We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…

Probability · Mathematics 2013-12-24 Nicolas Privault

We propose new summary measures of diagnostic test accuracy which can be used as companions to existing diagnostic accuracy measures. Conceptually, our summary measures are tantamount to the so-called Hellinger affinity and we show that…

Methodology · Statistics 2017-12-29 Miguel de Carvalho , Bradley J. Barney , Garritt L. Page