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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Exact tests for the means of Gaussian stochastic processes
TL;DR: In this article, the inferential properties of testing the means of Gaussian functional data, using a Mahalanobis type distance for Hilbert spaces, were investigated and the analytic power of exact and asymptotic tests, for the known and unknown covariance case, respectively.
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Simultaneous Confidence Bands for Functional Data Using the Gaussian Kinematic Formula
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Differential kinematic features of the hyoid bone during swallowing in patients with Parkinson's disease.
Woo Hyung Lee,Min Hyuk Lim,Hyung Seok Nam,Yoon Jae Kim,Han Gil Seo,Moon Suk Bang,Min Yong Seong,Byung Mo Oh,Sungwan Kim,Sungwan Kim +9 more
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A Spectral Representation of Kernel Stein Discrepancy with Application to Goodness-of-Fit Tests for Measures on Infinite Dimensional Hilbert Spaces
TL;DR: A novel spectral representation of KSD is provided, making KSD applicable to Hilbert-valued data and revealing the impact of kernel and Stein operator choice on the KSD.
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On functional data analysis and related topics
TL;DR: In this article , various contributions to the Special Issue of the Journal of Multivariate Analysis on Functional Data Analysis and some related topics including high-dimensional statistics and multivariate analysis of complex data are presented.
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