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We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…

Statistics Theory · Mathematics 2020-11-02 Clément Berenfeld , Marc Hoffmann

In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated possesses the single-index structure where neither the link function nor the index…

Statistics Theory · Mathematics 2013-04-26 Oleg Lepski , Nora Serdyukova

In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated has the "single-index" structure where neither the link function nor the index vector…

Statistics Theory · Mathematics 2013-04-30 Oleg Lepski , Nora Serdyukova

This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…

Statistics Theory · Mathematics 2017-04-17 Oleg Lepski , Thomas Willer

This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…

Statistics Theory · Mathematics 2025-07-17 Karine Bertin , Lisandro Fermin , Miguel Padrino

Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…

Machine Learning · Computer Science 2025-12-17 Sunia Tanweer , Firas A. Khasawneh

The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…

Numerical Analysis · Mathematics 2019-06-21 Adi Ditkowski , Gadi Fibich , Amir Sagiv

In the multidimensional setting, we consider the errors-in-variables model. We aim at estimating the unknown nonparametric multivariate regression function with errors in the covariates. We devise an adaptive estimator based on projection…

Statistics Theory · Mathematics 2016-01-13 Michaël Chichignoud , Van Ha Hoang , Thanh Mai Pham Ngoc , Vincent Rivoirard

We address the problem of adaptive minimax estimation in white gaussian noise model under $L_p$--loss, $1\leq p\leq\infty,$ on the anisotropic Nikolskii classes. We present the estimation procedure based on a new data-driven selection…

Statistics Theory · Mathematics 2014-05-20 Oleg Lepski

We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…

Statistics Theory · Mathematics 2025-09-30 Sergio Brenner Miguel , Jan Johannes , Maximilian Siebel

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…

Machine Learning · Computer Science 2025-06-04 Aleix Boquet-Pujadas , Pol del Aguila Pla , Michael Unser

This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density…

Statistics Theory · Mathematics 2023-01-10 Jeong Min Jeon , Ingrid Van Keilegom

In this work, we study wavelet projection estimators for density estimation, focusing on their construction from $\mathcal{S}$-regular, compactly supported wavelet bases. A key aspect of such estimators is the choice of the resolution…

Statistics Theory · Mathematics 2025-09-10 Van Ha Hoang , Tien Dat Nguyen , Thi Mong Ngoc Nguyen

The theory of adaptive estimation and oracle inequalities for the case of Gaussian-shift--finite-interval experiments has made significant progress in recent years. In particular, sharp-minimax adaptive estimators and exact exponential-type…

Statistics Theory · Mathematics 2008-12-18 Sam Efromovich

We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…

Methodology · Statistics 2023-09-22 Abhik Ghosh , Maria Jaenada , Leandro Pardo

A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…

Statistics Theory · Mathematics 2021-02-08 Gaelle Chagny , Antoine Channarond , Van Ha Hoang , Angelina Roche

This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth…

Statistics Theory · Mathematics 2016-04-04 Karine Bertin , Nicolas Klutchnikoff

We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent observations. The unknown density is assumed to be uniformly bounded and to belong to the…

Statistics Theory · Mathematics 2024-05-28 Galatia Cleanthous , Athanasios G. Georgiadis , Oleg V. Lepski

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

Statistics Theory · Mathematics 2024-04-19 Raphaël Maillet , Grégoire Szymanski

We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…

Methodology · Statistics 2020-01-09 Xianzheng Huang , Haiming Zhou