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We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…

Statistics Theory · Mathematics 2016-10-26 Mathieu Sart

This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both…

Statistics Theory · Mathematics 2025-07-22 Karine Bertin , Nicolas Klutchnikoff , Frédéric Ouimet

This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…

Statistics Theory · Mathematics 2020-07-07 Xiaowei Yang , Huiming Zhang , Haoyu Wei , Shouzheng Zhang

In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy…

Numerical Analysis · Mathematics 2022-02-28 Tim Jahn

Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…

Statistics Theory · Mathematics 2008-12-18 Sam Efromovich

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96…

Statistics Theory · Mathematics 2009-08-14 Hui Zou , Hao Helen Zhang

We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piecewise affine.…

Statistics Theory · Mathematics 2019-10-21 Oliver Y. Feng , Adityanand Guntuboyina , Arlene K. H. Kim , Richard J. Samworth

In this paper we consider the problem of estimating $f$, the conditional density of $Y$ given $X$, by using an independent sample distributed as $(X,Y)$ in the multivariate setting. We consider the estimation of $f(x,.)$ where $x$ is a…

Statistics Theory · Mathematics 2014-12-30 Karine Bertin , Claire Lacour , Vincent Rivoirard

We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…

Machine Learning · Statistics 2024-02-15 Mark Kozdoba , Binyamin Perets , Shie Mannor

An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…

Statistics Theory · Mathematics 2008-12-18 Leonid Galtchouk , Serguey Pergamenshchikov

We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…

Methodology · Statistics 2017-11-17 Wesley Tansey , Alex Athey , Alex Reinhart , James G. Scott

We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…

Statistics Theory · Mathematics 2019-03-15 Min Xu , Richard J. Samworth

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Computation · Statistics 2021-04-08 Richard J Clancy , Stephen Becker

We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a…

Statistics Theory · Mathematics 2021-02-15 Zaid Harchaoui , Anatoli Juditsky , Arkadi Nemirovski , Dmitrii Ostrovskii

We consider here estimation of an unknown probability density s belonging to L2(mu) where mu is a probability measure. We have at hand n i.i.d. observations with density s and use the squared L2-norm as our loss function. The purpose of…

Statistics Theory · Mathematics 2013-01-22 Lucien Birgé

We construct an adaptive estimator of a density function on $d$ dimensional unit sphere $S^d$ ($d \geq 2 $), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet…

Statistics Theory · Mathematics 2018-10-15 Bogdan Ćmiel , Karol Dziedziul , Natalia Jarzębkowska

The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…

Statistics Theory · Mathematics 2020-08-26 Alexander Goldenshluger , Oleg Lepski

We consider non parametric estimation problem for stochastic tomography regression model, i.e. we consider the estimation problem of function of multivariate variables (image) observed through its Radon transformation calculated with the…

Statistics Theory · Mathematics 2018-11-22 Dominique Fourdrinier , Sergey Pergamenshchikov

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…

Statistics Theory · Mathematics 2016-04-08 Nicolas Asin , Jan Johannes

Given a random sample from some unknown density $f_0: \mathbb R \to [0, \infty)$ we devise Haar wavelet estimators for $f_0$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny…

Statistics Theory · Mathematics 2012-02-23 Florian Gach , Richard Nickl , Vladimir Spokoiny