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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…

Statistics Theory · Mathematics 2009-09-29 Lawrence D. Brown , M. Levine

We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics…

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating an unknown nonparametric regression. %\cite{GaPe1}. We prove that this procedure is asymptotically efficient for a…

Statistics Theory · Mathematics 2010-02-09 Leonid Galtchouk , Serguei Pergamenchtchikov

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

Statistics Theory · Mathematics 2021-11-01 Keli Guo , Jun Fan , Lixing Zhu

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…

Statistics Theory · Mathematics 2009-04-06 Markus Reiss , Yves Rozenholc , Charles-Andre Cuenod

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

Statistics Theory · Mathematics 2014-06-17 Yun Yang , David B. Dunson

Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…

Statistics Theory · Mathematics 2025-02-27 Shunxing Yan , Fang Yao , Hang Zhou

We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…

Statistics Theory · Mathematics 2018-10-26 Ursula U. Müller , Anton Schick , Wolfgang Wefelmeyer

This paper considers nonparametric identification and estimation of the regression function when a covariate is mismeasured. The measurement error need not be classical. Employing the small measurement error approximation, we establish…

Econometrics · Economics 2024-03-19 Kirill S. Evdokimov , Andrei Zeleneev

In this paper, we propose a new test for the detection of a change in a non-linear (auto-)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at-most-one-change…

Statistics Theory · Mathematics 2025-04-15 Claudia Kirch , Stefanie Schwaar

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…

Econometrics · Economics 2020-06-15 Nishanth Dikkala , Greg Lewis , Lester Mackey , Vasilis Syrgkanis

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 propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Statistics Theory · Mathematics 2007-12-18 Jiming Jiang , Yihui Luan , You-Gan Wang

We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…

Statistics Theory · Mathematics 2016-08-16 Stéphane Gaiffas

We study in-context learning for nonparametric regression with $\alpha$-H\"older smooth regression functions, for some $\alpha>0$. We prove that, with $n$ in-context examples and $d$-dimensional regression covariates, a pretrained…

Machine Learning · Statistics 2026-05-20 Michelle Ching , Ioana Popescu , Nico Smith , Tianyi Ma , William G. Underwood , Richard J. Samworth

We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…

Statistics Theory · Mathematics 2008-12-17 Elisabeth Gassiat , Benoit Landelle

We discuss local linear smooth backfitting for additive non-parametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each…

Statistics Theory · Mathematics 2022-01-27 Munir Hiabu , Enno Mammen , Joseph T. Meyer

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…

Statistics Theory · Mathematics 2007-08-22 Ming-Yen Cheng , Liang Peng , Jyh-Shyang Wu

The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some…

Pricing of Securities · Quantitative Finance 2009-08-03 Denis Belomestny

A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…

Statistics Theory · Mathematics 2022-05-17 Christof Schötz