Related papers: Nonparametric estimation of composite functions
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…
Currently, the high-precision estimation of nonlinear parameters such as Gini indices, low-income proportions or other measures of inequality is particularly crucial. In the present paper, we propose a general class of estimators for such…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…
In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…
It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…
Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
In this paper we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function depends only on at most $s < d$ of the covariates, which is a special case…
We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the null hypothesis states that the regression function $f$…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
We discuss local linear smooth backfitting for additive non-parametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each…
We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…
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…
This article studies the recovery of graphons when they are convolution kernels on compact (symmetric) metric spaces. This case is of particular interest since it covers the situation where the probability of an edge depends only on some…
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
Many modern statistical estimation problems are defined by three major components: a statistical model that postulates the dependence of an output variable on the input features; a loss function measuring the error between the observed…