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Review of Functional Data Analysis
TLDR
An overview of FDA is provided, 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), an important dimension reduction tool and in sparse data situations can be used to impute functional data that are sparsely observed.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. They are both examples of "functional data", which have become a prevailing 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 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 data. Beyond linear and single or multiple index methods we touch upon a few nonlinear approaches that are promising for certain applications. They include additive and other nonlinear functional regression models, such as time warping, manifold learning, and dynamic modeling with empirical differential equations. The paper concludes with a brief discussion of future directions.read more
Citations
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A Course In Functional Analysis
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Model-based clustering for multivariate functional data
TL;DR: In this paper, a model-based clustering algorithm for multivariate functional data is proposed, based on the assumption of normality of the principal component scores, is defined and estimated by an EM-like algorithm.
Journal ArticleDOI
Recent advances in functional data analysis and high-dimensional statistics
TL;DR: This paper provides a structured overview of the contents of this Special Issue of the Journal of Multivariate Analysis devoted to Functional Data Analysis and Related Topics, along with a brief survey of the field.
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Methods for scalar-on-function regression
TL;DR: Some of the main approaches to how to fit regression models with scalar responses and functional data points as predictors are reviewed, categorizing the basic model types as linear, nonlinear and nonparametric.
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A general framework for functional regression modelling
Sonja Greven,Fabian Scheipl +1 more
TL;DR: A comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data is discussed, allowing the adaptation of a large body of existing methods for these novel tasks.
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