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We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…

Statistics Theory · Mathematics 2011-12-30 Marc Hoffmann , Axel Munk , Johannes Schmidt-Hieber

This paper considers nonparametric identification and estimation of the regression function when a covariate is mismeasured. The measurement error need not be classical. Employing the small measurement error approximation, we establish…

Econometrics · Economics 2024-03-19 Kirill S. Evdokimov , Andrei Zeleneev

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…

Statistics Theory · Mathematics 2015-09-25 Markus Reiß , Leonie Selk

A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…

Probability · Mathematics 2014-03-13 Bruno Saussereau

Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…

Methodology · Statistics 2007-10-30 Y. Pokern , A. M. Stuart , P. Wiberg

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…

Statistics Theory · Mathematics 2026-02-12 Hyeok Kyu Kwon , Dongha Kim , Ilsang Ohn , Minwoo Chae

The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…

Applications · Statistics 2016-04-01 Jakub Chorowski

In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm…

Numerical Analysis · Mathematics 2014-11-24 Olli Mali

We consider the graphon mean-field system introduced in the work of Bayraktar, Chakraborty, and Wu. It is the large-population limit of a heterogeneously interacting diffusive particle system, where the interaction is of mean-field type…

Statistics Theory · Mathematics 2024-03-12 Erhan Bayraktar , Hongyi Zhou

Modeling the complex interactions of systems of particles or agents is a fundamental scientific and mathematical problem that is studied in diverse fields, ranging from physics and biology, to economics and machine learning. In this work,…

Machine Learning · Statistics 2020-10-09 Jason Miller , Sui Tang , Ming Zhong , Mauro Maggioni

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…

Statistics Theory · Mathematics 2015-12-29 Teppei Ogihara

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…

Statistics Theory · Mathematics 2022-09-28 Wenlong Mou , Martin J. Wainwright , Peter L. Bartlett

Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…

Statistical Mechanics · Physics 2022-09-20 Seeralan Sarvaharman , Luca Giuggioli

In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…

Statistics Theory · Mathematics 2025-04-16 Mika Meitz , Alexander Shapiro

Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…

Methodology · Statistics 2018-12-04 Linh Nghiem , Michael Byrd , Cornelis Potgieter

We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…

Soft Condensed Matter · Physics 2024-10-03 Dev Jasuja , Paul J. Atzberger

This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…

Statistics Theory · Mathematics 2015-10-05 Jean-François Coeurjolly , Frédéric Lavancier

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

Statistics Theory · Mathematics 2016-11-18 XuanLong Nguyen , Martin J. Wainwright , Michael I. Jordan

In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…

Methodology · Statistics 2025-09-26 Miguel Alvarez , Ajay Jasra

Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To…

Methodology · Statistics 2021-01-15 Shonosuke Sugasawa , Kosuke Morikawa , Keisuke Takahata