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We introduce a robust and fully adaptive method for pointwise estimation in heteroscedastic regression. We allow for noise and design distributions that are unknown and fulfill very weak assumptions only. In particular, we do not impose…

Statistics Theory · Mathematics 2014-07-10 Michaël Chichignoud , Johannes Lederer

We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle…

Methodology · Statistics 2022-06-29 Anna Bonnet , Claire Lacour , Franck Picard , Vincent Rivoirard

In the Gaussian white noise model, we study the estimation of an unknown multidimensional function $f$ in the uniform norm by using kernel methods. The performances of procedures are measured by using the maxiset point of view: we determine…

Statistics Theory · Mathematics 2007-06-13 Karine Bertin , Vincent Rivoirard

In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…

Statistics Theory · Mathematics 2007-06-13 Pierre Alquier

We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…

Statistics Theory · Mathematics 2014-10-02 Moritz Jirak , Alexander Meister , Markus Reiß

This paper deals with the nonparametric estimation in heteroscedastic regression $ Y_i=f(X_i)+\xi_i, \: i=1,...,n $, with incomplete information, i.e. each real random variable $ \xi_i $ has a density $ g_{i} $ which is unknown to the…

Statistics Theory · Mathematics 2011-05-10 Michaël Chichignoud

In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete return distribution (denoted $\eta^\pi$) attained…

Machine Learning · Statistics 2025-11-13 Liangyu Zhang , Yang Peng , Jiadong Liang , Wenhao Yang , Zhihua Zhang

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…

Data Structures and Algorithms · Computer Science 2015-06-03 Jayadev Acharya , Ilias Diakonikolas , Jerry Li , Ludwig Schmidt

Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They…

Statistics Theory · Mathematics 2016-07-25 Shashank Singh , Simon S. Du , Barnabás Póczos

Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…

Artificial Intelligence · Computer Science 2013-01-18 Luis E. Ortiz , Leslie Pack Kaelbling

Sup-norm curve estimation is a fundamental statistical problem and, in principle, a premise for the construction of confidence bands for infinite-dimensional parameters. In a Bayesian framework, the issue of whether the…

Methodology · Statistics 2016-03-22 Catia Scricciolo

The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…

Data Structures and Algorithms · Computer Science 2021-09-06 Vladimir Braverman , Viska Wei , Samson Zhou

Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…

Statistics Theory · Mathematics 2026-05-06 Yannick Baraud

We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…

Numerical Analysis · Mathematics 2017-08-03 Alejandro Allendes , Enrique Otarola , Richard Rankin

Estimating parameters from samples of an optimal probability distribution is essential in applications ranging from socio-economic modeling to biological system analysis. In these settings, the probability distribution arises as the…

Machine Learning · Computer Science 2025-08-19 Francisco Andrade , Gabriel Peyré , Clarice Poon

This paper describes an adaptive method in continuous time for the estimation of external fields by a team of $N$ agents. The agents $i$ each explore subdomains $\Omega^i$ of a bounded subset of interest $\Omega\subset X := \mathbb{R}^d$.…

Systems and Control · Electrical Eng. & Systems 2021-03-24 Jia Guo , Michael E. Kepler , Sai Tej Paruchuri , Haoran Wang , Andrew J. Kurdila , Daniel J. Stilwell

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd…

Numerical Analysis · Mathematics 2020-09-07 Gregor Gantner , Dirk Praetorius

A compound Poisson process whose jump measure and intensity are unknown is observed at finitely many equispaced times. We construct a purely data-driven estimator of the L\'evy density $\nu$ through the spectral approach using general…

Statistics Theory · Mathematics 2019-02-12 Alberto J. Coca

In this paper, we study the problem of pointwise estimation of a multivariate density. We provide a data-driven selection rule from the family of kernel estimators and derive for it a pointwise oracle inequality. Using the latter bound, we…

Statistics Theory · Mathematics 2015-09-21 Gilles Rebelles

In this paper we consider a class of nonparametric estimators of a distribution function F, with compact support, based on the theory of IFSs. The estimator of F is tought as the fixed point of a contractive operator T defined in terms of a…

Statistics Theory · Mathematics 2007-06-13 Stefano M. Iacus , Davide La Torre