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Related papers: Adaptive functional linear regression

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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

This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…

Statistics Theory · Mathematics 2018-04-10 Hisayuki Tsukuma

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…

Methodology · Statistics 2021-11-03 Ufuk Beyaztas , Han Lin Shang

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS…

We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…

Methodology · Statistics 2024-12-17 Oliver Y. Feng , Yining Chen , Qiyang Han , Raymond J. Carroll , Richard J. Samworth

We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…

Statistics Theory · Mathematics 2015-03-13 Jan Johannes , Maik Schwarz

This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…

Statistics Theory · Mathematics 2025-07-17 Karine Bertin , Lisandro Fermin , Miguel Padrino

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…

Statistics Theory · Mathematics 2017-03-09 Qingguo Tang , Linglong Kong , David Ruppert , Rohana J. Karunamuni

We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…

Methodology · Statistics 2016-10-05 Anirvan Chakraborty , Victor M. Panaretos

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

Statistics Theory · Mathematics 2025-06-03 Yannick Baraud , Guillaume Maillard

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

Methodology · Statistics 2009-02-20 Aurore Delaigle , Peter Hall , Tatiyana V. Apanasovich

This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional…

Statistics Theory · Mathematics 2013-02-28 Kengo Kato

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…

Statistics Theory · Mathematics 2024-03-29 T. Tony Cai , Dongwoo Kim , Hongming Pu

Consider the case that we observe $n$ independent and identically distributed copies of a random variable with a probability distribution known to be an element of a specified statistical model. We are interested in estimating an infinite…

Statistics Theory · Mathematics 2017-09-20 Mark J. van der Laan , Aurélien F. Bibaut

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

Methodology · Statistics 2021-08-27 Ioannis Kalogridis , Stefan Van Aelst

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…

Statistics Theory · Mathematics 2022-02-10 Christoph Breunig , Xiaohong Chen

The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations,…

Methodology · Statistics 2025-12-02 Ufuk Beyaztas , Han Lin Shang , Gizel Bakicierler Sezer

Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…

Statistics Theory · Mathematics 2018-09-19 Sneha Jadhav , Shuangge Ma

The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…

Statistics Theory · Mathematics 2013-01-22 Xiao Wang , David Ruppert

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

Statistics Theory · Mathematics 2024-09-18 Ling Peng , Xiaohui Liu , Heng Lian