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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Basis expansions for functional snippets
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Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines
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Quantifying and Visualizing Intraregional Connectivity in Resting-State Functional Magnetic Resonance Imaging with Correlation Densities.
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Functional variable selection via Gram–Schmidt orthogonalization for multiple functional linear regression
TL;DR: In this paper, a new functional linear model is proposed for high-throughput studies such as meteorological and biomedical research, which is of great practical importance, as exemplified by applications in high throughput studies.
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