Related papers: Concentration Inequalities and Confidence Bands fo…

Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-H\"older balls, $0<t\le r$, where $r$ is a…

Confidence bands are confidence sets for an unknown function f, containing all functions within some sup-norm distance of an estimator. In the density estimation, regression, and white noise models, we consider the problem of constructing…

The problem of estimating a probability density function f on the (d-1)-dimensional unit sphere S^{d-1} from directional data using the needlet frame is considered. It is shown that the decay of needlet coefficients supported near a point…

We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine…

We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article…

Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable…

The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…

We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…

In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\top\beta$ is positive.The vectors $X$ and $\beta$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$.We prove lower…

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…

Given a random sample from some unknown density $f_0: \mathbb R \to [0, \infty)$ we devise Haar wavelet estimators for $f_0$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny…

Let $f$ be a probability density and $C$ be an interval on which $f$ is bounded away from zero. By establishing the limiting distribution of the uniform error of the kernel estimates $f_n$ of $f$, Bickel and Rosenblatt (1973) provide…

A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…

We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…

The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of…

This paper develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on…

We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. Our method integrates sieve…

This paper develops a method to construct uniform confidence bands for a nonparametric regression function where a predictor variable is subject to a measurement error. We allow for the distribution of the measurement error to be unknown,…

This paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete…

Given $n$ i.i.d. observations, we study the problem of estimating the spectrum of weighted Laplace operators of the form $\Delta_f=\Delta + \alpha \nabla \log f\cdot \nabla$, where $f$ is a positive probability density on a known compact…