Related papers: Minimax and Adaptive Inference in Nonparametric Fu…
In ill-posed imaging inverse problems, uncertainty quantification remains a fundamental challenge, especially in safety-critical applications. Recently, conformal prediction has been used to quantify the uncertainty that the inverse problem…
This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…
The paper discusses inference techniques for semiparametric models based on suitable versions of inference functions. The text contains two parts. In the first part, we review the optimality theory for non-parametric models based on the…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…
This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…
The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…
We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…
Predicting scalar outcomes using functional predictors is a classic problem in functional data analysis. In many applications, however, only specific locations or time-points of the functional predictors have an impact on the outcome. Such…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to…
We consider the problem of combining data from observational and experimental sources to make causal conclusions. This problem is increasingly relevant, as the modern era has yielded passive collection of massive observational datasets in…
We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…
We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares estimator and obtain component-wise and…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…
The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…