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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Testing for lack-of-fit in functional regression models against general alternatives
TL;DR: In this paper, a lack-of-fit test for functional regression models is proposed, which is based on the fact that checking the noeffect of a functional covariate is equivalent to checking the nullity of the conditional expectation of the error term given a sufficiently rich set of projections of that covariate.
Journal ArticleDOI
Functional Data Visualization and Outlier Detection on the Anomaly of El Niño Southern Oscillation
TL;DR: In this article, the authors adopted functional data analysis theory by representing a multivariate ENSO index (MEI) as functional data in climate applications and found that the outliers obtained from the functional plot are then related to the El Nino and La Nina phenomena.
Posted Content
Clustering multivariate functional data using unsupervised binary trees.
TL;DR: A model-based clustering algorithm for a general class of functional data for which the components could be curves or images, and is applied to the analysis of vehicle trajectories on a German roundabout.
Journal ArticleDOI
Dimension reduction for functional data based on weak conditional moments
TL;DR: Weak conditional expectation as discussed by the authors is a generalization of conditional expectation, which replaces the projection on to an L 2-space by projection on an arbitrary Hilbert space, while still maintaining the unbiasedness of the related dimension reduction methods.
Journal ArticleDOI
High-dimensional MANOVA via Bootstrapping and its Application to Functional and Sparse Count Data
TL;DR: A new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors that is able to provide dimension-free and nearly-parametric convergence rates for Gaussian approximation, bootstrap approximation, and the size of the test.
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