Related papers: Minimax and Adaptive Inference in Nonparametric Fu…

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…

Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…

This paper considers adaptive, minimax estimation of a quadratic functional in a nonparametric instrumental variables (NPIV) model, which is an important problem in optimal estimation of a nonlinear functional of an ill-posed inverse…

The paper is devoted to the problem of estimation of a univariate component in a heteroscedastic nonparametric multiple regression under the mean integrated squared error (MISE) criteria. The aim is to understand how the scale function…

A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are…

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic…

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…

Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…

Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…

Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…

In a remarkable series of papers beginning in 1956, Charles Stein set the stage for the future development of minimax shrinkage estimators of a multivariate normal mean under quadratic loss. More recently, parallel developments have seen…

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…

Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…