English
Related papers

Related papers: On nonparametric estimation of the interaction fun…

200 papers

We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…

Statistics Theory · Mathematics 2009-09-29 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

Optimization and Control · Mathematics 2013-12-19 J. C. Jimenez

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

Methodology · Statistics 2017-04-03 Nina Munkholt Jakobsen , Michael Sørensen

We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…

Numerical Analysis · Mathematics 2024-01-30 Grigorios A. Pavliotis , Andrea Zanoni

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…

Optimization and Control · Mathematics 2026-03-31 José A. Carrillo , Shi Jin , Haoyu Zhang , Yuhua Zhu

Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…

Statistics Theory · Mathematics 2021-07-02 T. Tony Cai , Hongji Wei

This study introduces a nonparametric definition of interaction and provides an approach to both interaction discovery and efficient estimation of this parameter. Using stochastic shift interventions and ensemble machine learning, our…

Methodology · Statistics 2024-07-01 David B. McCoy , Alan E. Hubbard , Alejandro Schuler , Mark J. van der Laan

A method is proposed for estimating the potential function of a non-parametric estimator for stationary and isotropic pairwise interaction point process. The relation between a pair potential and the corresponding Papangelou conditional…

Probability · Mathematics 2015-06-08 Nadia Morsli

We introduce a new method for online parameter estimation in stochastic interacting particle systems, based on continuous observation of a small number of particles from the system. Our method recursively updates the model parameters using…

Statistics Theory · Mathematics 2026-02-25 Louis Sharrock , Nikolas Kantas , Grigorios A. Pavliotis

This paper presents a new parameter estimation method for It\^{o} diffusions such that the resulting model predicts the equilibrium statistics as well as the sensitivities of the underlying system to external disturbances. Our formulation…

Numerical Analysis · Mathematics 2017-05-24 John Harlim , Xiantao Li , He Zhang

We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…

Statistics Theory · Mathematics 2022-01-20 Tetsuya Kawai , Masayuki Uchida

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…

Statistics Theory · Mathematics 2007-06-13 Ilia Negri

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

Data Analysis, Statistics and Probability · Physics 2016-01-05 Elliot A. Martin , Jaroslav Hlinka , Alexander Meinke , Filip Děchtěrenko , Jörn Davidsen

Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…

Machine Learning · Statistics 2026-05-15 Ayoub Belhadji , Daniel Sharp , Youssef M. Marzouk

We study parameter estimation for interacting particle systems (IPSs) consisting of $N$ weakly interacting multivariate hypoelliptic SDEs. We propose a locally Gaussian approximation of the transition dynamics, carefully designed to address…

Statistics Theory · Mathematics 2025-09-19 Yuga Iguchi , Alexandros Beskos , Grigorios A. Pavliotis

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…

Statistical Mechanics · Physics 2025-04-15 Roberto da Silva , Eliseu Venites Filho , Henrique Almeida Fernandes , Paulo F. Gomes

This paper studies the problem of nonparametric estimation of a smooth function with data distributed across multiple machines. We assume an independent sample from a white noise model is collected at each machine, and an estimator of the…

Machine Learning · Statistics 2018-06-26 Yuancheng Zhu , John Lafferty

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

Statistics Theory · Mathematics 2022-03-02 Gaëlle Chagny , Anouar Meynaoui , Angelina Roche

In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…

Statistics Theory · Mathematics 2026-03-31 Chiara Amorino , Vytautė Pilipauskaitė