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We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…

Probability · Mathematics 2013-04-18 Kaspar Stucki , Dominic Schuhmacher

We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include…

Machine Learning · Statistics 2022-10-25 Victor Chernozhukov , Whitney Newey , Rahul Singh

Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…

Methodology · Statistics 2024-09-06 Fernando Baltazar-Larios , Mogens Bladt , Michael Sørensen

Let $Y$ be a $d$-dimensional random vector with unknown mean $\mu$ and covariance matrix $\Sigma$. This paper is motivated by the problem of designing an estimator of $\Sigma$ that admits tight deviation bounds in the operator norm under…

Statistics Theory · Mathematics 2018-03-09 Stanislav Minsker , Xiaohan Wei

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of…

Statistics Theory · Mathematics 2013-06-25 Michal Pešta

Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…

Numerical Analysis · Mathematics 2024-03-18 Edward J. Fuselier , John Paul Ward

One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…

Statistics Theory · Mathematics 2025-02-14 Jonathan R. Stewart

We investigate the estimation of a small interaction parameter from the outcomes of weak quantum measurements implemented by the interaction. The relation of weak values and sensitivity is explained and the different contributions of…

Quantum Physics · Physics 2012-10-23 Holger F. Hofmann , Michael E. Goggin , Marcelo P. Almeida , Marco Barbieri

We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…

Statistics Theory · Mathematics 2021-06-07 Lin Liu , Rajarshi Mukherjee , James Robins , Eric Tchetgen Tchetgen

This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…

Statistics Theory · Mathematics 2024-02-23 Denis Belomestny , Mark Podolskij , Shi-Yuan Zhou

The robustness of properties of a statistical physics model to slight perturbations in the exact local interactions of the model is a very relevant philosophical question, considering real-life measurements on which we base some models can…

Mathematical Physics · Physics 2025-07-25 Léo Gayral , Mathieu Sablik

Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…

Methodology · Statistics 2015-06-23 Carlo Berzuini , A. Philip Dawid

In experiments that study social phenomena, such as peer influence or herd immunity, the treatment of one unit may influence the outcomes of others. Such "interference between units" violates traditional approaches for causal inference, so…

Methodology · Statistics 2023-08-30 David Choi

The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…

Statistical Mechanics · Physics 2014-01-30 Benaoumeur Bakhti , Michael Karbach , Philipp Maass , Mohammad Mokim , Gerhard Muller

In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…

Statistics Theory · Mathematics 2014-08-15 Axel Bücher , Johan Segers , Stanislav Volgushev

In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…

Probability · Mathematics 2017-01-05 Tanguy Cabana , Jonathan Touboul

This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…

Statistics Theory · Mathematics 2015-07-29 Emanuele Taufer

We derive an asymptotic power function for a likelihood-based test for interaction in a regression model, with possibly misspecified alternative distribution. This allows a general investigation of types of interactions which are poorly or…

Statistics Theory · Mathematics 2007-11-27 Juxin Liu , Paul Gustafson

Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…

Probability · Mathematics 2015-04-29 Farida Kachapova , Ilias Kachapov