Related papers: A sharp adaptive confidence ball for self-similar …

Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different…

In a Riemannian manifold, it is well known that the scalar curvature at a point can be recovered from the volumes (areas) of small geodesic balls (spheres). We show the scalar curvature is likewise determined by the relative capacities of…

Astronomers often deal with data where the covariates and the dependent variable are measured with heteroscedastic non-Gaussian error. For instance, while TESS and Kepler datasets provide a wealth of information, addressing the challenges…

This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…

Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…

This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…

We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric…

It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is…

Constructing nonasymptotic confidence intervals (CIs) for the mean of a univariate distribution from independent and identically distributed (i.i.d.) observations is a fundamental task in statistics. For bounded observations, a classical…

In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…

We investigate the relationship between the compactness of embeddings of Sobolev spaces built upon rearrangement-invariant spaces into rearrangement-invariant spaces endowed with $d$-Ahlfors measures under certain restriction on the speed…

Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…

Consider a sequence of estimators $\hat \theta_n$ which converges almost surely to $\theta_0$ as the sample size $n$ tends to infinity. Under weak smoothness conditions, we identify the asymptotic limit of the last time $\hat \theta_n$ is…

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear…

We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…

First and second kind modifications of usual confidence intervals for estimating the expectation and of usual local alternative parameter choices are introduced in a way such that the asymptotic behavior of the true non-covering…

Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is…