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The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

Methodology · Statistics 2025-11-27 Ioannis Kalogridis , Stanislav Nagy

We consider a bivariate time series $(X_t,Y_t)$ that is given by a simple linear autoregressive model. Assuming that the equations describing each variable as a linear combination of past values are considered structural equations, there is…

Statistics Theory · Mathematics 2018-04-12 Dominik Janzing , Paul Rubenstein , Bernhard Schölkopf

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

This paper addresses estimation in a longitudinal regression model for association between a scalar outcome and a set of longitudinally-collected functional covariates or predictor curves. The framework consists of estimating a time-varying…

Applications · Statistics 2020-06-30 Madan G. Kundu , Jaroslaw Harezlak , Timothy W. Randolph

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

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…

Statistics Theory · Mathematics 2024-11-08 Natalie Neumeyer , Leonie Selk

We describe a design-based framework for drawing causal inference in general randomized experiments. Causal effects are defined as linear functionals evaluated at unit-level potential outcome functions. Assumptions about the potential…

Methodology · Statistics 2025-08-15 Christopher Harshaw , Fredrik Sävje , Yitan Wang

Regressing a scalar response on a random function is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression based on a projection approach a prominent method for solving…

Methodology · Statistics 2019-07-19 Frédéric Ferraty , Stanislav Nagy

The theory of linear Fredholm integral-functional equations of the second kind with linear functionals and with a parameter is considered. The necessary and sufficient conditions are obtained for the coefficients of the equation and those…

Mathematical Physics · Physics 2023-03-30 L. R. Dreglea Sidorov , N. Sidorov , D. Sidorov

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student $t$-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting…

Methodology · Statistics 2017-05-17 Chunzheng Cao , Jian Qing Shi , Youngjo Lee

By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…

Artificial Intelligence · Computer Science 2013-02-08 Paul-Andre Monney

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…

Machine Learning · Statistics 2013-01-16 Hachem Kadri , Philippe Preux , Emmanuel Duflos , Stéphane Canu

The functional logit regression model was proposed by Escabias et al. (2004) with the objective of modeling a scalar binary response variable from a functional predictor. The model estimation proposed in that case was performed in a…

Methodology · Statistics 2024-02-08 Manuel Escabias , Ana M. Aguilera , Christian Acal

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations.…

Methodology · Statistics 2025-11-03 Pavel Hernández-Amaro , Maria Durban , M. Carmen Aguilera-Morillo

We propose a flexible regression framework to model the conditional distribution of multilevel generalized multivariate functional data of potentially mixed type, e.g. binary and continuous data. We make pointwise parametric distributional…

Methodology · Statistics 2024-07-31 Alexander Volkmann , Nikolaus Umlauf , Sonja Greven

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

Methodology · Statistics 2025-07-08 Michael Lindon , Dae Woong Ham , Martin Tingley , Iavor Bojinov

The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…

Numerical Analysis · Mathematics 2022-10-27 Dmitry A. Skorik

Regression models to relate a scalar $Y$ to a functional predictor $X(t)$ are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, $\beta(t)$, with $Y$ related to $X(t)$ through…

Statistics Theory · Mathematics 2009-08-21 Gareth M. James , Jing Wang , Ji Zhu

In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…

Methodology · Statistics 2021-09-14 Ufuk Beyaztas , Han Lin Shang , Aylin Alin