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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Adaptive LASSO estimation for functional hidden dynamic geostatistical models
TL;DR: In this paper , a model selection algorithm based on a penalized maximum likelihood estimator for functional hidden dynamic geostatistical models (f-HDGM) is proposed, which employs a classic mixed-effect regression structure with embedded spatio-temporal dynamics to model georeferenced data observed in a functional domain.
Bayesian functional linear regression estimation. Extension to scalar and categorical covariates
TL;DR: Grollemund et al. as mentioned in this paper extend the Bliss method to a more general model that also contains categorical and scalar covariates, and propose an extension of the Bliss model and how to estimate the parameters in an interpretable way.
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Single-index partially functional linear quantile regression
Zhiqiang Jiang,Zhensheng Huang +1 more
TL;DR: In this paper , a single-index partially functional linear quantile regression is proposed, and B-splines are used to estimate the unknown link function and unknown slope function in the single index component and the unknown linear component, respectively.
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Curve Fitting Algorithm of Functional Radiation-Response Data Using Bayesian Hierarchical Gaussian Process Regression Model
TL;DR: In this paper , a nonparametric Bayesian hierarchical (NBH) model and a variational approximation (VA) algorithm for the curve fitting of the functional radiation response data are presented.
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Bi-Smoothed Functional Independent Component Analysis for EEG Artifact Removal
TL;DR: In this article, the spectral decomposition of the kurtosis operator of a smoothed principal component expansion is used to obtain the smoothed basis for the independent component model, and a discrete roughness penalty is introduced in the orthonormality constraint of the covariance eigenfunctions.
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