Related papers: Robust nonparametric estimation via wavelet median…
We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while…
We consider the non-parametric regression problem under Huber's $\epsilon$-contamination model, in which an $\epsilon$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing…
We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive…
This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric…
We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…
This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…
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 propose a wavelet-based technique for the nonparametric estimation of functions contaminated with noise whose mean and variance are linked via a possibly unknown variance function. Our method, termed the data-driven wavelet-Fisz…
With the ubiquitous availability of unstructured data, growing attention is paid as how to adjust for selection bias in such non-probability samples. The majority of the robust estimators proposed by prior literature are either fully or…
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…
We construct efficient robust truncated sequential estimators for the pointwise estimation problem in nonparametric autoregression models with smooth coefficients. For Gaussian models we propose an adaptive procedure based on the…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…