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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Proceedings ArticleDOI
Recognizing Commutator Motors Fault from Acoustics Signals Using Bayesian Functional Data Depth
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Estimation of trace-variogram using Legendre–Gauss quadrature
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Bayesian function registration with random truncation
TL;DR: In this paper , a Gaussian process prior is assigned to the parameter space of time warping functions, and a Markov chain Monte Carlo (MCMC) algorithm is utilized to explore the posterior distribution.
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A link function specification test in the single functional index model
TL;DR: In this article , a test for specification in functional regression with scalar response that exploits semi-parametric principles is illustrated, and its asymptotic null distribution is derived under suitable conditions.
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A fast epigraph and hypograph-based approach for clustering functional data
TL;DR: In this paper , the epigraph and hypograph indexes are applied to the original curves and to their first and/or second derivatives to transform the information given by the functional data to the multivariate context, being informative enough for the usual multivariate clustering techniques to be efficient.
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