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Related papers: Prediction in functional linear regression

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We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…

Statistics Theory · Mathematics 2012-02-24 Jean-Yves Audibert , Olivier Catoni

In this paper, we study the estimation of the derivative of a regression function in a standard univariate regression model. The estimators are defined either by derivating nonparametric least-squares estimators of the regression function…

Statistics Theory · Mathematics 2023-11-13 Fabienne Comte , Nicolas Marie

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…

Statistics Theory · Mathematics 2016-08-16 Peter Hall , Hans-Georg Müller , Jane-Ling Wang

We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the…

Statistics Theory · Mathematics 2016-01-27 Qiyang Han , Jon A. Wellner

We consider the minimization of composite objective functions composed of the expectation of quadratic functions and an arbitrary convex function. We study the stochastic dual averaging algorithm with a constant step-size, showing that it…

Optimization and Control · Mathematics 2017-02-22 Nicolas Flammarion , Francis Bach

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…

Statistics Theory · Mathematics 2015-03-20 Adam D. Bull

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…

Statistics Theory · Mathematics 2011-11-29 Heng Lian

We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that…

Statistics Theory · Mathematics 2017-09-01 Qiyang Han , Tengyao Wang , Sabyasachi Chatterjee , Richard J. Samworth

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

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

This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…

Machine Learning · Computer Science 2017-11-09 Daniel Hsu , Kevin Shi , Xiaorui Sun

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…

Statistics Theory · Mathematics 2013-08-07 Aboubacar Amiri , Christophe Crambes , Baba Thiam

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…

Statistics Theory · Mathematics 2017-05-29 Forzani Liliana , Fraiman Ricardo , Llop Pamela

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…

Statistics Theory · Mathematics 2016-04-08 Nicolas Asin , Jan Johannes

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…

Statistics Theory · Mathematics 2016-08-16 Fang Yao , Hans-Georg Müller , Jane-Ling Wang

Centering is a commonly used technique in linear regression analysis. With centered data on both the responses and covariates, the ordinary least squares estimator of the slope parameter can be calculated from a model without the intercept.…

Methodology · Statistics 2022-10-04 HaiYing Wang

Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…

Methodology · Statistics 2025-08-19 Ioannis Kalogridis

Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…

Methodology · Statistics 2020-08-17 Neil Shephard

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

Methodology · Statistics 2009-05-20 F. Bunea , M. H. Wegkamp , A. E. Ivanescu

This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…

Statistics Theory · Mathematics 2020-11-23 Karine Bertin , Nicolas Klutchnikoff