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Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…

Methodology · Statistics 2024-11-26 Dan Yang , Jianlong Shao , Haipeng Shen , Hongtu Zhu

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…

Statistics Theory · Mathematics 2007-06-13 Hans-Georg Muller , Ulrich Stadtmuller

We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…

Statistics Theory · Mathematics 2014-10-02 Moritz Jirak , Alexander Meister , Markus Reiß

The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…

Statistics Theory · Mathematics 2025-10-29 Iryna Dubovets'ka , Mykhailo Moklyachuk

We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared…

Machine Learning · Statistics 2023-01-24 Rahul Parhi , Robert D. Nowak

We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…

Statistics Theory · Mathematics 2025-06-19 Thomas B. Berrett

Scalar-on-function logistic regression, where the response is a binary outcome and the predictor consists of random curves, has become a general framework to explore a linear relationship between the binary outcome and functional predictor.…

Methodology · Statistics 2022-04-07 Muge Mutis , Ufuk Beyaztas , Gulhayat Golbasi Simsek , Han Lin Shang

In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…

Statistics Theory · Mathematics 2020-11-16 Anuj Abhishek , Sakshi Arya

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

Machine Learning · Statistics 2025-11-20 Gábor Balázs

We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…

Statistics Theory · Mathematics 2016-01-12 Rajarshi Mukherjee , Eric Tchetgen Tchetgen , James Robins

In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…

Methodology · Statistics 2025-05-22 Minxuan Wu , Joseph Antonelli , Zhihua Su

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…

Methodology · Statistics 2023-09-25 Xuancheng Wang , Ling Zhou , Huazhen Lin

We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a…

Methodology · Statistics 2022-06-17 Adeline Fermanian

This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…

Statistics Theory · Mathematics 2021-10-19 Shaogao Lv , Xin He , Junhui Wang

This paper studies a regression model where both predictor and response variables are random functions. We consider a functional linear model where the conditional mean of the response variable at each time point is given by a linear…

Statistics Theory · Mathematics 2017-03-23 Masaaki Imaizumi , Kengo Kato

We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling but considering a functional data framework. The…

Statistics Theory · Mathematics 2013-02-06 Santiago Gallón , Jean-Michel Loubes , Fabrice Gamboa

This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…

Methodology · Statistics 2024-12-11 Yikun Zhang , Alexander Giessing , Yen-Chi Chen

We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…

Methodology · Statistics 2020-11-03 Edoardo Belli , Simone Vantini

In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…

Methodology · Statistics 2021-12-21 Yafei Wang , Tingyu Lai , Bei Jiang , Linglong Kong , Zhongzhan Zhang

The aim of this paper is to recover the regression function with sup norm loss. We construct an asymptotically sharp estimator which converges with the spatially dependent rate r\_{n, \mu}(x) = P \big(\log n / (n \mu(x)) \big)^{s / (2s +…

Statistics Theory · Mathematics 2016-08-16 Stéphane Gaiffas