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
Applications of functional data analysis: A systematic review.
Shahid Ullah,Caroline F. Finch +1 more
TL;DR: Despite its clear benefits for analyzing time series data, full appreciation of the key features and value of FDA have been limited to date, though the applications show its relevance to many public health and biomedical problems.
Journal ArticleDOI
From sparse to dense functional data and beyond
Xiaoke Zhang,Jane-Ling Wang +1 more
TL;DR: In this paper, the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight each subject (SUBJ), as two special cases, is investigated.
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.
Posted Content
Review of Functional Data Analysis
TL;DR: 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.
Journal ArticleDOI
Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study.
TL;DR: Overall, domain-general abilities were more important than domain-specific knowledge for mathematics learning in early grades but general abilities and domain- specific knowledge were equally important in later grades.
References
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Functional canonical analysis for square integrable stochastic processes
TL;DR: In this paper, the authors studied the functional canonical correlation from pairs of random vectors to the case where a data sample consists of pairs of square integrable stochastic processes.
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Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles
TL;DR: In this article, a test based on a Karhunen-loeve approximation of the Hilbert-Schmidt distance of the empirical covariance operators is proposed and investigated to determine whether the mechanical properties of short strands of DNA are significantly affected by their base-pair sequence.
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Functional Adaptive Model Estimation
TL;DR: In this article, a functional adaptive model estimation (FAME) approach is proposed to model the relationship between a scalar, Y, and a functional predictor, X(t), which extends generalized linear models, generalized additive models, and projection pursuit regression (PPR) to handle functional predictors.
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Defining probability density for a distribution of random functions
Aurore Delaigle,Peter A. Hall +1 more
TL;DR: In this paper, the authors developed the notion of density when functional data are considered in the space determined by the eigenfunctions of principal component analysis, which leads to a transparent and meaningful surrogate for density defined in terms of the average value of the logarithms of the densities of the distributions of principal components for a given dimension.
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Kernel-based functional principal components (
TL;DR: In this article, a kernel-based smooth estimate of the functional principal components of stochastic processes is proposed for continuous trajectories of continuous processes, and strong consistency and the asymptotic distribution are derived under mild conditions.