Related papers: Adaptive estimation of functionals in nonparametri…

We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…

A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…

Consider nonparametric function estimation under $L^p$-loss. The minimax rate for estimation of the regression function over a H\"older ball with smoothness index $\beta$ is $n^{-\beta/(2\beta+1)}$ if $1\leq p<\infty$ and $(n/\log…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…

We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and…

In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

The aim of this paper is to estimate the density f of a random variable X when one has access to independent observations of the sum of K $\ge$ 2 independent copies of X. We provide a constructive estimator based on a suitable definition of…

We consider the problem of adaptive estimation of the functional component in a multivariate partial linear model where the argument of the function is defined on a $q$-dimensional grid. Obtaining an adaptive estimator of this functional…

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…

This work deals with the ill-posed inverse problem of reconstructing a function $f$ given implicitly as the solution of $g = Af$, where $A$ is a compact linear operator with unknown singular values and known eigenfunctions. We observe the…

We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…

In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the…

The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…

We study the non-parametric estimation of the value ${\theta}(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed…

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…