Related papers: Intrinsic Riemannian Functional Data Analysis for …
In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen-Loeve…
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…
When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…
Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the local extrinsic and intrinsic curvature. We show that the…
Motivated by distinct walking patterns in real-world free-living gait data, this paper proposes an innovative curve-based sampling scheme for the analysis of functional data characterized by a mixture of covariance structures. Traditional…
This paper examines robust functional data analysis for discretely observed data, where the underlying process encompasses various distributions, such as heavy tail, skewness, or contaminations. We propose a unified robust concept of…
Extrinsic Gaussian process regression methods, such as wrapped Gaussian process, have been developed to analyze manifold data. However, there is a lack of intrinsic Gaussian process methods for studying complex data with manifold-valued…
In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…
In this paper, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We approach this problem…
Regression is an essential and fundamental methodology in statistical analysis. The majority of the literature focuses on linear and nonlinear regression in the context of the Euclidean space. However, regression models in non-Euclidean…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline…
Accurately specifying covariance structures is critical for valid inference in longitudinal and functional data analysis, particularly when data are sparsely observed. In this study, we develop a global goodness-of-fit test to assess…
The analysis of multivariate functional curves has the potential to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. However, it is common for real-world settings to present…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…