Related papers: The Mahalanobis distance for functional data with …

Statistical analysis on non-Euclidean spaces typically relies on distances as the primary tool for constructing likelihoods. However, manifold-valued data admits richer structures in addition to Riemannian distances. We demonstrate that…

Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

In this article we will present a new perspective on the variable order fractional calculus, which allows for differentiation and integration to a variable order, i.e. one differentiates (or integrates) a function along the path of a…

For statistical inference on an infinite-dimensional Hilbert space $\H $ with no moment conditions we introduce a new class of energy distances on the space of probability measures on $\H$. The proposed distances consist of the integrated…

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…

General estimates from below of holomorphic and subharmonic functions play one of the key roles in the theory of growth of holomorphic and subharmonic functions and in general in the theory of potential. At the same time, the most diverse…

Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…

The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…

In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…

As a measure for the centrality of a point in a set of multivariate data, statistical depth functions play important roles in multivariate analysis, because one may conveniently construct descriptive as well as inferential procedures…

We propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random series priors based on a…

This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction with the advent of modern complex observation systems. Here, particular interest is in evaluating whether two sets of…

The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…

We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…

Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…