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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Functional repeated measures analysis of variance and its application
TL;DR: In this paper , a pointwise test statistic is constructed by adapting the classical test statistic for one-way repeated measures analysis of variance to the functional data framework, which can be represented as functions.
An Empirical Investigation of Intergenerational Mobility in Korea
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A functional data feature learning method with EM algorithm in industrial soft sensing modeling
Xiaoying Tan,Wei Guo,Ran Liu +2 more
TL;DR: In this article , the functional probabilistic principal component analysis (FPPCA) is introduced to handle process noise in industrial process data, and a loglikelihood function involved in functional data is designed, and the regression model parameters can then be estimated through the expectation maximization (EM) algorithm, iteratively.
C 4 interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters
TL;DR: In this article , a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed, and the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data.
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