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
Estimation and Hypothesis Test for Mean Curve with Functional Data by Reproducing Kernel Hilbert Space Methods, with Applications in Biostatistics
TL;DR: In this article , the authors developed a general framework for a mean curve estimation for functional data using a reproducing kernel Hilbert space (RKHS) and derive its asymptotic distribution theory.
Mixture of multivariate gaussian processes for classification of irregularly sampled satellite image time-series
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Book ChapterDOI
Continuous-Time Autoregressive Moving-Average Processes in Hilbert Space
Fred Espen Benth,André Süss +1 more
TL;DR: In this article, the authors introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces and consider Levy processes as driving noises of these processes.
Journal ArticleDOI
Bayesian inference and dynamic prediction of multivariate joint model with functional data: An application to Alzheimer's disease
TL;DR: In this article, a multivariate joint model with functional data (MJM-FD) framework was proposed to predict individual's future longitudinal outcomes and risk of a survival event in Alzheimer's disease.
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