Related papers: On convex regression estimators
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…
Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…
A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and…
In this paper, we focus on regression estimation in both the inductive and the transductive case. We assume that we are given a set of features (which can be a base of functions, but not necessarily). We begin by giving a deviation…
A new way to design parameter estimators with enhanced performance is proposed in the paper. The procedure consists of two stages, first, the generation of new regression forms via the application of a dynamic operator to the original…
The extremal dependence structure of a regularly varying random vector Xis fully described by its limiting spectral measure. In this paper, we investigate how torecover characteristics of the measure, such as extremal coefficients, from the…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…