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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funcharts: control charts for multivariate functional data in R
Christian Capezza,Fábio Centofanti,Antonio Lepore,Alessandra Menafoglio,Biagio Palumbo,Simone Vantini +5 more
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Truncated estimation for varying-coefficient functional linear model
TL;DR: In this article , a truncated estimation method for varying-coefficient functional linear models is proposed to clarify to what time point the functional predictor relates to the response at any value of the exogenous variable by investigating the coefficient function.
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Two-sample Functional Linear Models
TL;DR: In this article, the authors study two-sample functional linear regression with a scaling transformation of regression functions and investigate semiparametric efficiency for the estimation of the scalar parameter and hypothesis testing.
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Variograms for kriging and clustering of spatial functional data with phase variation
TL;DR: In this paper , a decomposition of the trace-variogram into amplitude and phase components is proposed to quantify how spatial correlations between functional observations manifest in their respective amplitude and phases.
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