Functional Data Analysis
TLDR
In this article, the authors provide an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA).Abstract:
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. These are both examples of functional data, which has become a commonly encountered type of data. Functional data analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysis and theory of data that are in the form of functions. This paper provides an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA). FPCA is an important dimension reduction tool, and in sparse data situations it can be used to impute functional data that are sparsely observed. Other dimension reduction approaches are also discussed. In addition, we review another core technique, functional linear regression, as well as clustering and classification of functional d...read more
Citations
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Journal ArticleDOI
Multivariate Functional Data Modeling with Time-varying Clustering
Philip A. White,Alan E. Gelfand +1 more
TL;DR: In this paper, the authors consider the situation where multivariate functional data has been collected over time at each of a set of sites and implement model-based clustering of the functions across the sites.
Journal ArticleDOI
Fixed‐effects inference and tests of correlation for longitudinal functional data
TL;DR: In this article , an inferential framework for fixed effects in longitudinal functional models and tests for the correlation structures induced by the longitudinal sampling procedure is proposed, which provides a natural extension of standard longitudinal correlation models for scalar observations to functional observations.
Journal ArticleDOI
LESA: Longitudinal Elastic Shape Analysis of Brain Subcortical Structures
TL;DR: The authors developed a simple and efficient framework of longitudinal elastic shape analysis (LESA) for subcortical structures, integrating ideas from elastic shapes analysis of static surfaces and statistical modeling of sparse longitudinal data, and applied LESA to analyze three longitudinal neuroimaging datasets and showcase its wide applications in estimating continuous shape trajectories.
Posted Content
Functional Principal Component Analysis for Extrapolating Multi-stream Longitudinal Data
Seokhyun Chung,Raed Kontar +1 more
TL;DR: In this article, a Gaussian process prior for the FPC scores is established based on a functional semi-metric that measures similarities between streams of historical units and the in-service unit.
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Spatiotemporal Covariance Estimation by Shifted Partial Tracing
Tomas Masak,Victor M. Panaretos +1 more
TL;DR: Non-parametric estimators hinging on the novel concept of shifted partial tracing are introduced, which is capable of estimating the model computationally efficiently under dense observation, and are shown to yield consistent estimators of the separable part of the covariance even under noisy discrete observation.
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