Related papers: Lower bounds for volatility estimation in microstr…
Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as noise, hold the…
For the problem of nonparametric estimation of signal in Gaussian noise we point out the strong asymptotically minimax estimators on maxisets for linear estimators (see \cite{ker93,rio}). It turns out that the order of rates of convergence…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
Inspired by the notion that environmental noise is in principle observable, whilst fundamental noise due to spontaneous localisation would not be, we study the estimation of the diffusion parameter induced by wave function collapse models…
A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic…
Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…
In this paper, we derive minimax rates for estimating both parametric and nonparametric components in partially linear additive models with high dimensional sparse vectors and smooth functional components. The minimax lower bound for…
We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…
We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…
We first revisit the problem of estimating the spot volatility of an It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel. Next, we introduce a new…
In this letter, we address the problem of estimating Gaussian noise level from the trained dictionaries in update stage. We first provide rigorous statistical analysis on the eigenvalue distributions of a sample covariance matrix. Then we…
The CSL model predicts a progressive breakdown of the quantum superposition principle, with a noise randomly driving the state of the system towards a localized one, thus accounting for the emergence of a classical world within a quantum…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…
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…
Ill-posed inverse problems arise in various scientific fields. We consider the signal detection problem for mildly, severely and extremely ill-posed inverse problems with $l^q$-ellipsoids (bodies), $q\in(0,2]$, for Sobolev, analytic and…
In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp…
The optimization of black-box functions with noisy observations is a fundamental problem with widespread applications, and has been widely studied under the assumption that the function lies in a reproducing kernel Hilbert space (RKHS).…
Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to L\'evy-driven…