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We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

Probability · Mathematics 2017-04-28 Aneta Buraczyńska , Anna Dembińska

Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…

Populations and Evolution · Quantitative Biology 2022-04-27 Alexander Krauß , Thilo Gross , Barbara Drossel

In this paper, we explore the two-star Exponential Random Graph Model, which is a two parameter exponential family on the space of simple labeled graphs. We introduce auxiliary variables to express the two-star model as a mixture of the…

Statistics Theory · Mathematics 2021-03-04 Sumit Mukherjee , Yuanzhe Xu

We present an extension of the ergodic, mixing and Bernoulli levels of the ergodic hierarchy in dynamical systems, the information geometric ergodic hierarchy (IGEH), making use of statistical models on curved manifolds in the context of…

Mathematical Physics · Physics 2017-06-28 Ignacio S. Gomez , Mariela Portesi

This paper deals with empirical processes of the type \[C_n(B)=\sqrt{n}\{\mu_n(B)-P(X_{n+1}\in B\mid X_1,...,X_n)\},\] where $(X_n)$ is a sequence of random variables and $\mu_n=(1/n)\sum_{i=1}^n\delta_{X_i}$ the empirical measure.…

Statistics Theory · Mathematics 2010-01-14 Patrizia Berti , Irene Crimaldi , Luca Pratelli , Pietro Rigo

We prove the asymptotic independence of the empirical process $\alpha_n = \sqrt{n}( F_n - F)$ and the rescaled empirical distribution function $\beta_n = n (F_n(\tau+\frac{\cdot}{n})-F_n(\tau))$, where $F$ is an arbitrary cdf,…

Probability · Mathematics 2015-06-16 Dietmar Ferger , Daniel Vogel

Unmeasured spatial confounding complicates exposure effect estimation in environmental health studies. This problem is exacerbated in studies with multiple health outcomes and environmental exposure variables, as the source and magnitude of…

This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $\beta N \to const \in (0, \infty)$, with $N$ the system size and $\beta$ the inverse temperature. In this regime, the convergence to…

Probability · Mathematics 2020-04-17 Fumihiko Nakano , Khanh Duy Trinh

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…

Probability · Mathematics 2013-11-26 Jonathan C. Mattingly , Andrew M. Stuart , M. V. Tretyakov

The experimental and theoretical challenges posed by the study of dynamically inhomogeneous systems are outlined in the context of cuprates and other oxides. Considering the pitfalls in the single-component approach to the analysis of…

Superconductivity · Physics 2007-05-23 D. Mihailovic

Superstatistics [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a superposition of…

Statistical Mechanics · Physics 2018-08-07 F. Sattin

Statistical matching aims to integrate two statistical sources. These sources can be two samples or a sample and the entire population. If two samples have been selected from the same population and information has been collected on…

Methodology · Statistics 2023-01-04 Raphaël Jauslin , Yves Tillé

Concentration inequalities have become increasingly popular in machine learning, probability, and statistical research. Using concentration inequalities, one can construct confidence intervals (CIs) for many quantities of interest.…

Statistics Theory · Mathematics 2019-03-06 Hien D. Nguyen

Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This…

Statistics Theory · Mathematics 2016-11-21 Johan Segers , Masaaki Sibuya , Hideatsu Tsukahara

We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…

Probability · Mathematics 2022-03-10 Svante Janson

The asymptotic validity of a resampling method for two sequential processes constructed from non-degenerate $U$-statistics is established under mixing conditions. The resampling schemes, referred to as {\em dependent multiplier bootstraps},…

Statistics Theory · Mathematics 2015-05-29 Axel Bücher , Ivan Kojadinovic

We prove a new concentration inequality for U-statistics of order two for uniformly ergodic Markov chains. Working with bounded and $\pi$-canonical kernels, we show that we can recover the convergence rate of Arcones and Gin{\'e} who proved…

Probability · Mathematics 2022-03-21 Quentin Duchemin , Yohann de Castro , Claire Lacour

Tests of equality of copulas between two samples are introduced and studied using the empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a subsampling Bernstein…

Statistics Theory · Mathematics 2023-12-19 Guanjie Lyu , Mohamed Belalia

We study the effect of strategic behavior in iterative voting for multiple issues under uncertainty. We introduce a model synthesizing simultaneous multi-issue voting with Meir, Lev, and Rosenschein (2014)'s local dominance theory and…

Computer Science and Game Theory · Computer Science 2023-01-24 Joshua Kavner , Reshef Meir , Francesca Rossi , Lirong Xia

The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…

Numerical Analysis · Mathematics 2018-01-30 Yanan Jiang , Wei Liu , Lihui Weng