Related papers: Functional data analysis in the Banach space of co…
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…
For sequentially observed functional data exhibiting multiple change points in the mean function, we establish consistency results for the estimated number and locations of the change points based on the norm of the functional CUSUM process…
In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…
It is of great interest to test the equality of the means in two samples of functional data. Past research has predominantly concentrated on low-dimensional functional data, a focus that may not hold up in high-dimensional scenarios. In…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
Motivated by the need to statistically quantify differences between modern (complex) data-sets which commonly result as high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to…
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…
This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude…
This paper makes 3 contributions. First, it generalizes the Lindeberg\textendash Feller and Lyapunov Central Limit Theorems to Hilbert Spaces by way of $L^2$. Second, it generalizes these results to spaces in which sample failure and…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally…
Data depth is a powerful nonparametric tool originally proposed to rank multivariate data from center outward. In this context, one of the most archetypical depth notions is Tukey's halfspace depth. In the last few decades notions of depth…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…
In Euclidean space of dimension 2 or 3, we study a minimum time problem associated with a system of real-analytic vector fields satisfying H\"ormander's bracket generating condition, where the target is a nonempty closed set. We show that,…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…
We introduce the $\mathcal{L}^p$ spaces of measurable functions whose $p$-th power is summable with respect to the uniform measure over the Levi-Civita field $\mathcal{R}$. These spaces are the counterparts of the real $L^p$ spaces based…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The…