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In this paper, I study the nonparametric identification and estimation of the marginal effect of an endogenous variable $X$ on the outcome variable $Y$, given a potentially mismeasured instrument variable $W^*$, without assuming linearity…

Econometrics · Economics 2024-04-23 Shaomin Wu

In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…

Methodology · Statistics 2017-11-15 Behdad Mostafaiy , MohammadReza FaridRohani , Shojaeddin Chenouri

In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…

Methodology · Statistics 2020-03-03 Li Cai , Lijie Gu , Qihua Wang , Suojin Wang

This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however…

Statistics Theory · Mathematics 2008-02-22 Joseph Rynkiewicz

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Peter Hall

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…

Statistics Theory · Mathematics 2025-08-27 Tien Dat Nguyen , Thanh Mai Pham Ngoc

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…

Statistics Theory · Mathematics 2025-04-24 Xiong Wang , Inbar Seroussi , Fei Lu

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

Statistics Theory · Mathematics 2009-02-26 Christophe Crambes , Alois Kneip , Pascal Sarda

This work concerns the estimation of multidimensional nonlinear regression models using multilayer perceptrons (MLPs). The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator.…

Statistics Theory · Mathematics 2008-02-22 Joseph Rynkiewicz

When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…

Statistics Theory · Mathematics 2017-05-17 François Portier , Johan Segers

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

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…

Statistics Theory · Mathematics 2015-12-01 Yuchen Zhang , Martin J. Wainwright , Michael I. Jordan

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Statistics Theory · Mathematics 2022-07-05 Yuliana Linke , Igor Borisov , Pavel Ruzankin , Vladimir Kutsenko , Elena Yarovaya , Svetlana Shalnova

The goal of nonparametric regression is to recover an underlying regression function from noisy observations, under the assumption that the regression function belongs to a pre-specified infinite dimensional function space. In the online…

Methodology · Statistics 2021-04-05 Tianyu Zhang , Noah Simon

We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require…

Machine Learning · Statistics 2024-05-31 Xuxing Chen , Abhishek Roy , Yifan Hu , Krishnakumar Balasubramanian

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…

Machine Learning · Statistics 2020-10-13 Viet Anh Nguyen , Fan Zhang , Jose Blanchet , Erick Delage , Yinyu Ye

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…

Statistics Theory · Mathematics 2020-12-01 Koohyun Kwon , Soonwoo Kwon

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…

Machine Learning · Statistics 2015-05-14 Xinyang Yi , Zhaoran Wang , Constantine Caramanis , Han Liu

We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied…

Econometrics · Economics 2024-10-18 Samuele Centorrino , Frédérique Fève , Jean-Pierre Florens

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…

Statistics Theory · Mathematics 2019-07-16 Martin Kroll