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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Journal ArticleDOI
OUP accepted manuscript
TL;DR: In this paper , a functional hybrid factor regression model was proposed to handle the heterogeneity of many large-scale imaging studies, such as the Alzheimer's disease neuroimaging initiative study.
Proceedings ArticleDOI
Similarity-based Prognostics for Remaining Useful Life Prediction of Engineered Systems
TL;DR: In this paper , a similarity-based prognostic approach for accurate RUL prediction is presented, where historical degradation trajectories are properly abstracted into the common degrading characteristics (i.e., one mean trend and a few varying modes) for the whole system population by functional principal component analysis, so that the capacity of degradation trajectory library is greatly reduced.
Journal ArticleDOI
Two-sample functional linear models with functional responses
TL;DR: In this article , the authors proposed two-sample functional linear regression models with functional responses, where the regression functions are assumed to have a scaling transformation, and they estimate the intercept function, slope function, and parameter components based on the least squares method and functional principal component analysis.
Journal ArticleDOI
Coastal environmental and atmospheric data reduction in the Southern North Sea supporting ecological impact studies
TL;DR: In this paper, dimension reduction techniques are applied to environmental data simulated by the Delft3D coastal water quality model, the HIRLAM numerical weather prediction model and the Euro-CORDEX climate modelling experiment.
Journal ArticleDOI
Additive hazards model with time-varying coefficients and imaging predictors
TL;DR: Wang et al. as mentioned in this paper developed a two-stage approach that comprises the high-dimensional functional principal component analysis technique in the first stage and the counting process-based estimating equation approach in the second stage.
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