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This article studies global testing of the slope function in functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The…

Statistics Theory · Mathematics 2021-10-13 Jianjun Xu , Wenquan Cui

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…

Statistics Theory · Mathematics 2012-04-03 Klaus Frick , Philipp Marnitz , Axel Munk

Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…

Optimization and Control · Mathematics 2025-05-30 Tran T. A. Nghia , Huy N. Pham , Nghia V. Vo

Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…

Statistics Theory · Mathematics 2013-01-16 Elodie Brunel , André Mas , Angelina Roche

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

Statistics Theory · Mathematics 2013-02-19 Michael Vogt

Discrete-time affine processes are widely used in finance and economics and encompass count, positive, and nonnegative-valued processes. This paper develops near-unit-root asymptotic theory for this class of models. Unlike linear AR(1)…

Statistics Theory · Mathematics 2026-05-28 Gael Anne , Yang Lu , Xuewen Yu , Xiaowen Zhou

This paper presents new results on prediction of linear processes in function spaces. The autoregressive Hilbertian process framework of order one (ARH(1) process framework) is adopted. A componentwise estimator of the autocorrelation…

Statistics Theory · Mathematics 2018-09-05 J. Álvarez-Liébana , D. Bosq , M. Dolores Ruiz-Medina

The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…

Methodology · Statistics 2023-07-26 Lorenzo Lucchese , Mikko S. Pakkanen , Almut E. D. Veraart

In modern biomedical and econometric studies, longitudinal processes are often characterized by complex time-varying associations and abrupt regime shifts that are shared across correlated outcomes. Standard functional data analysis (FDA)…

Methodology · Statistics 2026-01-28 Baolin Chen , Mengfei Ran

We consider the problem of estimating the autocorrelation operator of an autoregressive Hilbertian process. By means of a Tikhonov approach, we establish a general result that yields the convergence rate of the estimated autocorrelation…

Statistics Theory · Mathematics 2022-06-09 Alessia Caponera , Victor M. Panaretos

We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…

Methodology · Statistics 2022-07-19 Peijun Sang , Bing Li

Spatially distributed functional data are prevalent in many statistical applications such as meteorology, energy forecasting, census data, disease mapping, and neurological studies. Given their complex and high-dimensional nature,…

Statistics Theory · Mathematics 2024-02-06 Suneel Babu Chatla , Ruiqi Liu

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…

Numerical Analysis · Mathematics 2024-10-14 Michael Kartmann , Tim Keil , Mario Ohlberger , Stefan Volkwein , Barbara Kaltenbacher

In this paper we derive the asymptotic distributions of two distinct regularized estimators for functional canonical correlation as well as their associated eigenvalues, eigenvectors and projection operators. The methods we developed…

Statistics Theory · Mathematics 2015-02-10 David B. King

This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…

Methodology · Statistics 2014-04-01 Alexander Aue , Diogo Dubart Norinho , Siegfried Hörmann

Matrix-variate time series data are increasingly popular in economics, statistics, and environmental studies, among other fields. This paper develops regularized estimation methods for analyzing high-dimensional matrix-variate time series…

Methodology · Statistics 2024-10-16 Hangjin Jiang , Baining Shen , Yuzhou Li , Zhaoxing Gao

A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…

Methodology · Statistics 2018-08-21 Alessio Sancetta

Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement model for an unknown function $u(x)$ is \begin{eqnarray*}…

Analysis of PDEs · Mathematics 2016-06-03 Hanne Kekkonen , Matti Lassas , Samuli Siltanen

Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The…

Statistics Theory · Mathematics 2018-11-16 Johannes T. N. Krebs , Jürgen E. Franke

Conditional stability estimates are a popular tool for the regularization of ill-posed problems. A drawback in particular under nonlinear operators is that additional regularization is needed for obtaining stable approximate solutions if…

Numerical Analysis · Mathematics 2019-05-29 Daniel Gerth , Bernd Hofmann , Christopher Hofmann