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Motivated by change point problems in time series and the detection of textured objects in images, we consider the problem of detecting a piece of a Gaussian Markov random field hidden in white Gaussian noise. We derive minimax lower bounds…

Statistics Theory · Mathematics 2015-10-15 Ery Arias-Castro , Sébastien Bubeck , Gábor Lugosi , Nicolas Verzelen

We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…

Probability · Mathematics 2020-01-16 Martin Sauer , Wilhelm Stannat

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction…

Statistics Theory · Mathematics 2019-12-02 Boualem Djehiche , Othmane Mazhar , Cristian R. Rojas

This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…

Statistics Theory · Mathematics 2023-05-03 David Azriel

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

Machine Learning · Computer Science 2026-05-12 Johannes Teutsch , Oleksii Molodchyk , Marion Leibold , Timm Faulwasser , Armin Lederer

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

Numerical Analysis · Mathematics 2018-02-14 Simon Arridge , Kazufumi Ito , Bangti Jin , Chen Zhang

Structure-agnostic causal inference studies how well one can estimate a treatment effect given black-box machine learning estimates of nuisance functions (like the impact of confounders on treatment and outcomes). Here, we find that the…

Machine Learning · Statistics 2025-11-10 Jikai Jin , Lester Mackey , Vasilis Syrgkanis

The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust…

Information Theory · Computer Science 2010-05-03 Wenyi Zhang , H. Vincent Poor

In this paper, we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book. The tests compare two distinct quasi-maximum…

Statistical Finance · Quantitative Finance 2019-02-20 Simon Clinet , Yoann Potiron

A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…

Statistics Theory · Mathematics 2018-04-27 Victor-Emmanuel Brunel , Jason M. Klusowski , Dana Yang

We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which…

Statistics Theory · Mathematics 2025-08-12 Marc Hoffmann , Kolyan Ray

We consider a model where a signal (discrete or continuous) is observed with an additive Gaussian noise process. The signal is issued from a linear combination of a finite but increasing number of translated features. The features are…

Statistics Theory · Mathematics 2024-07-23 Cristina Butucea , Jean-François Delmas , Anne Dutfoy , Clément Hardy

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…

Systems and Control · Electrical Eng. & Systems 2026-05-20 Felix Brändle , Nicolas Chatzikiriakos , Andrea Iannelli , Frank Allgöwer

A technique for on-line estimation of spot volatility for high-frequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction.…

Methodology · Statistics 2013-01-15 Rainer Dahlhaus , Jan C. Neddermeyer

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Statistics Theory · Mathematics 2017-12-05 Shogo H. Nakakita , Masayuki Uchida

We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The methods…

Applications · Statistics 2016-02-02 Georgi Dinolov , Abel Rodriguez , Hongyun Wang

In this paper, based on a known formula, we use a simple idea to get a new representation for the density of Malliavin differentiable random variables. This new representation is particularly useful for finding lower bounds for the density.

Probability · Mathematics 2019-12-23 Nguyen Tien Dung

Detection of an image boundary when the pixel intensities are measured with noise is an important problem in image segmentation, with numerous applications in medical imaging and engineering. From a statistical point of view, the challenge…

Methodology · Statistics 2020-12-11 Nicholas Syring , Ryan Martin

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…

Information Theory · Computer Science 2022-05-19 Adrien Vandenbroucque , Amedeo Roberto Esposito , Michael Gastpar

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