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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TL;DR: In this paper, a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function is proposed, where a linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function, and the expected value of the response is related to this linear predictor via a link function.
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Inference for Density Families Using Functional Principal Component Analysis
TL;DR: In this article, a detailed asymptotic theory is presented for the analysis of yearly cross-sectional samples of British households from 1968-1988, which provides new insights into the evolution and interplay of household income and age distributions.
Journal ArticleDOI
Nonparametric Regression Analysis of Growth Curves
TL;DR: In this article, the authors presented that kernel estimates of acceleration and velocity of height, and of height itself, might offer advantages over a parametric fitting via functional models, but the parametric one shows qualitative and quantitative distortion which both are not easily predictable.