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The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density…

Statistics Theory · Mathematics 2012-02-27 I. Dattner , A. Goldenshluger , A. Juditsky

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

We consider the random design regression model with square loss. We propose a method that aggregates empirical minimizers (ERM) over appropriately chosen random subsets and reduces to ERM in the extreme case, and we establish sharp oracle…

Statistics Theory · Mathematics 2017-07-04 Alexander Rakhlin , Karthik Sridharan , Alexandre B. Tsybakov

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

Statistics Theory · Mathematics 2024-01-05 Y. Baraud , H. Halconruy , G. Maillard

We focus on the nonparametric density estimation problem with directional data. We propose a new rule for bandwidth selection for kernel density estimation. Our procedure is automatic, fully data-driven and adaptive to the smoothness degree…

Statistics Theory · Mathematics 2018-08-08 Thanh Mai Pham Ngoc

We investigate the problem of estimating a function $f$ based on observations from its noisy convolution when the noise exhibits long-range dependence. We construct an adaptive estimator based on the kernel method, derive minimax lower…

Statistics Theory · Mathematics 2017-06-28 Rida Benhaddou

The problem of estimation of analytic density function using L_p minimax risk is considered. A kernel-type estimator of an unknown density function is proposed and the upper bound on its limiting local minimax risk is established. Our…

Statistics Theory · Mathematics 2011-10-11 Natalia Stepanova

This paper deals with non-parametric density estimation on $\bR^2$ from i.i.d observations. It is assumed that after unknown rotation of the coordinate system the coordinates of the observations are independent random variables whose…

Statistics Theory · Mathematics 2020-02-26 Lepski O. V. , Rebelles G

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 model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…

Statistics Theory · Mathematics 2016-09-29 Pierre C. Bellec

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from…

Statistics Theory · Mathematics 2009-08-26 Vladimir Spokoiny , Céline Vial

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

Statistics Theory · Mathematics 2017-03-28 Vlad Barbu , Slim Beltaif , Serguei Pergamenchtchikov

This paper addresses the problem of model selection in the sequence model $Y=\theta+\varepsilon\xi$, when $\xi$ is sub-Gaussian, for non-euclidian loss-functions. In this model, the Penalized Comparison to Overfitting procedure is studied…

Statistics Theory · Mathematics 2025-04-16 Claire Lacour , Pascal Massart , Vincent Rivoirard

The performance of Least Squares (LS) estimators is studied in isotonic, unimodal and convex regression. Our results have the form of sharp oracle inequalities that account for the model misspecification error. In isotonic and unimodal…

Statistics Theory · Mathematics 2016-08-09 Pierre C. Bellec

We consider a circular deconvolution problem, in which the density $f$ of a circular random variable $X$ must be estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y$ of $X$. The additive measurement error is…

Statistics Theory · Mathematics 2013-12-11 Jan Johannes , Maik Schwarz

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

We study the problem of linear and convex aggregation of $M$ estimators of a density with respect to the mean squared risk. We provide procedures for linear and convex aggregation and we prove oracle inequalities for their risks. We also…

Statistics Theory · Mathematics 2007-06-13 Philippe Rigollet , Alexandre Tsybakov

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…

Statistics Theory · Mathematics 2024-06-04 Thijs Bos , Johannes Schmidt-Hieber

In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge,…

Statistics Theory · Mathematics 2013-01-15 Felix Abramovich , Marianna Pensky , Yves Rozenholc

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