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Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…

Statistics Theory · Mathematics 2019-11-15 Angshuman Roy , Anil Ghosh , Alok Goswami , C. A. Murthy

A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…

Probability · Mathematics 2019-04-29 Sebastian Engelke , Thomas Opitz , Jennifer Wadsworth

We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…

Statistics Theory · Mathematics 2020-10-23 F. Richard Guo , Thomas S. Richardson

Several general trends have been identified for equilibrated, self-gravitating collisionless systems, such as density or anisotropy profiles. These are integrated quantities which naturally depend on the underlying velocity distribution…

Astrophysics · Physics 2009-11-11 Steen H. Hansen , Ben Moore , Marcel Zemp , Joachim Stadel

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…

Statistics Theory · Mathematics 2020-06-15 Kayvan Sadeghi

A seminal result in the ICA literature states that for $AY = \varepsilon$, if the components of $\varepsilon$ are independent and at most one is Gaussian, then $A$ is identified up to sign and permutation of its rows (Comon, 1994). In this…

Statistics Theory · Mathematics 2024-03-21 Geert Mesters , Piotr Zwiernik

In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…

Probability · Mathematics 2020-08-25 Youri Davydov , Svyatoslav Novikov

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…

Machine Learning · Statistics 2016-09-14 Nguyen Tran Quang , Alexander Jung

We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…

Probability · Mathematics 2007-05-23 Ph . Barbe , W. P. McCormick , C. Zhang

We consider a string with fixed endpoints where the mass density and/or the elastic coefficient vary in a self-affine way as function of position. It is demonstrated how the eigenvalues in the asymptotic limit are distributed. Scaling laws…

Disordered Systems and Neural Networks · Physics 2007-05-23 Ingve Simonsen , Alex Hansen

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…

Methodology · Statistics 2016-04-04 Anindya Bhadra , Arvind Rao , Veerabhadran Baladandayuthapani

We consider the stochastic behavior of a class of local $U$-statistics of Poisson processes$-$which include subgraph and simplex counts as special cases, and amounts to quantifying clustering behavior$-$for point clouds lying in diverging…

Probability · Mathematics 2022-07-25 Andrew M. Thomas

For an underactuated (simple) Hamiltonian system with two degrees of freedom and one degree of underactuation, a rather general condition that ensures its stabilizability, by means of the existence of a (simple) Lyapunov function, was found…

Optimization and Control · Mathematics 2019-04-29 Sergio Grillo , Leandro Salomone , Marcela Zuccalli

Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…

Statistics Theory · Mathematics 2024-09-12 Sebastian Engelke , Jevgenijs Ivanovs , Kirstin Strokorb

We derive a powerful yet simple method for analyzing the local density of states in gapless one dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the…

Strongly Correlated Electrons · Physics 2010-01-19 Imke Schneider , Sebastian Eggert

The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…

Dynamical Systems · Mathematics 2017-11-07 Rachid Bouyekhf , Lyubomir T. Gruyitch

Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…

Statistics Theory · Mathematics 2017-02-02 Bikramjit Das , Sidney I. Resnick

It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables get asymptotically independent as the sample size increases.…

Statistics Theory · Mathematics 2017-02-01 Michael Falk , Florian Wisheckel

We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is…

Probability · Mathematics 2014-05-12 Jaakko Lehtomaa

It is shown that a Wishart matrix of standard complex normal random variables is asymptotically freely independent of an independent random matrix, under minimal conditions, in two different sense of asymptotic free independence.

Probability · Mathematics 2018-02-06 Arijit Chakrabarty , Sukrit Chakraborty , Rajat Subhra Hazra