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In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under high-dimensional multivariate functional data setting.…

Methodology · Statistics 2022-05-04 Ali Mahzarnia , Jun Song

Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…

Machine Learning · Computer Science 2025-07-11 Erfan Mirzaei , Andreas Maurer , Vladimir R. Kostic , Massimiliano Pontil

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…

Statistics Theory · Mathematics 2018-01-04 Andrea Ghiglietti , Francesca Ieva , Anna Maria Paganoni , Giacomo Aletti

In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…

Statistics Theory · Mathematics 2021-04-14 Shahin Tavakoli , Gilles Nisol , Marc Hallin

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Machine Learning · Statistics 2025-03-19 Minoru Kusaba , Megumi Iwayama , Ryo Yoshida

We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…

Statistics Theory · Mathematics 2026-05-05 Kou Fujimori , Koji Tsukuda

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

High-dimensional functional data are becoming increasingly common in fields such as environmental monitoring and neuroimaging. This paper studies high-dimensional functional linear regression models that relate a scalar response to…

Methodology · Statistics 2026-05-08 Xingche Guo , Yehua Li , Pang Du

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…

Methodology · Statistics 2024-01-19 Jonas Krampe , Efstathios Paparoditis

The semiparametric regression models have attracted increasing attention owing to their robustness compared to their parametric counterparts. This paper discusses the efficiency bound for functional response models (FRM), an emerging class…

Methodology · Statistics 2022-05-18 Jinyuan Liu , Tuo Lin , Tian Chen , Xinlian Zhang , Xin M. Tu

In the last few decades, building regression models for non-scalar variables, including time series, text, image, and video, has attracted increasing interests of researchers from the data analytic community. In this paper, we focus on a…

Machine Learning · Computer Science 2020-12-01 Qiyao Wang , Haiyan Wang , Chetan Gupta , Aniruddha Rajendra Rao , Hamed Khorasgani

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

Machine Learning · Statistics 2024-02-20 Jiading Liu , Lei Shi

The focus of the paper is functional output regression (FOR) with convoluted losses. While most existing work consider the square loss setting, we leverage extensions of the Huber and the $\epsilon$-insensitive loss (induced by infimal…

Machine Learning · Statistics 2022-06-17 Alex Lambert , Dimitri Bouche , Zoltan Szabo , Florence d'Alché-Buc

In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing…

Methodology · Statistics 2021-09-28 Mauro Bernardi , Antonio Canale , Marco Stefanucci

We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied…

Methodology · Statistics 2021-03-09 Peijun Sang , Adam B Kashlak , Linglong Kong

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

Statistics Theory · Mathematics 2023-02-07 Rafail Kartsioukas , Stilian Stoev , Tailen Hsing

Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional…

Statistics Theory · Mathematics 2012-11-22 Dong Chen , Peter Hall , Hans-Georg Müller

This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at different time lags are investigated in the topology of their…

Probability · Mathematics 2025-06-23 Marie-Christine Düker , Pavlos Zoubouloglou

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…

Methodology · Statistics 2023-01-12 Holger Dette , Gauthier Dierickx , Tim Kutta

In this paper, we study an additive model where the response variable is Hilbert-space-valued and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows to cover…

Statistics Theory · Mathematics 2022-12-13 Jeong Min Jeon , Germain Van Bever