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We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…

Statistics Theory · Mathematics 2007-06-13 Mohamed El Machkouri

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…

Statistics Theory · Mathematics 2023-11-02 Zhaoyang Shi , Krishnakumar Balasubramanian , Wolfgang Polonik

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive…

Statistics Theory · Mathematics 2007-06-13 Emmanuel Guerre , Pascal Lavergne

As computer resources become increasingly limited, traditional statistical methods face challenges in analyzing massive data, especially in functional data analysis. To address this issue, subsampling offers a viable solution by…

Methodology · Statistics 2024-07-01 Jingxiang Pan , Xiaohui Yuan , Xiaohui Yuan

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…

Statistics Theory · Mathematics 2016-02-02 Nicolas Asin , Jan Johannes

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…

Statistics Theory · Mathematics 2024-07-16 Céline Duval , Émeline Schmisser

Estimation of the mean and covariance functions is a fundamental problem in functional data analysis, particularly for discretely observed functional data. In this work, we study a regularization-based framework for estimating the mean and…

Statistics Theory · Mathematics 2026-03-20 Naveen Gupta , Bharath K Sriperumbudur

Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…

Methodology · Statistics 2025-04-07 Sunny G. W. Wang , Valentin Patilea , Nicolas Klutchnikoff

In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level $\lambda$. More precisely, it is assumed that the density (i) is smooth in a…

Statistics Theory · Mathematics 2016-09-07 Philippe Rigollet , Régis Vert

A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a…

Statistics Theory · Mathematics 2016-01-25 Tim Patschkowski , Angelika Rohde

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…

Statistics Theory · Mathematics 2016-08-16 D. Anevski , O. Hössjer

In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth…

Statistics Theory · Mathematics 2023-07-03 Tien Dat Nguyen , Thanh Mai Pham Ngoc , Vincent Rivoirard

Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…

Statistics Theory · Mathematics 2021-09-29 Holger Dette , Jiajun Tang

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…

We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite…

Machine Learning · Statistics 2019-06-11 Henry W J Reeve , Ata Kaban

The nonparametric regression with a random design model is considered. We want to recover the regression function at a point x where the design density is vanishing or exploding. Depending on assumptions on the regression function local…

Statistics Theory · Mathematics 2016-08-16 Stéphane Gaiffas

Nonparametric regression with random design is considered. The $L_2$ error with integration with respect to the design measure is used as the error criterion. An over-parametrized deep neural network regression estimate with logistic…

Statistics Theory · Mathematics 2025-04-07 Michael Kohler

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…

Statistics Theory · Mathematics 2010-10-21 Weidong Liu , Wei Biao Wu

This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…

Statistics Theory · Mathematics 2010-10-05 Rawane Samb

We consider nonparametric regression in the context of functional data, that is, when a random sample of functions is observed on a fine grid. We obtain a functional asymptotic normality result allowing to build simultaneous confidence…

Methodology · Statistics 2015-03-13 David A. Degras