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 data. Beyond linear and single- or multiple- index methods, we touch upon a few nonlinear approaches that are promising for certain applications. They include additive and other nonlinear functional regression models and models that feature time warping, manifold learning, and empirical differential equations. The paper concludes with a brief discussion of future directions.

Jane-Ling Wang

Jeng-Min Chiou

Hans-Georg Müller

Annual Review of Statistics and Its Application

统计及其应用年度回顾向统计学家和统计用户介绍主要方法学进展和允许实施的计算工具。

The Annual Review of Statistics and Its Application is an annual review journal that aims to introduce major methodological advancements in the field of statistics and the computational tools that facilitate their implementation to statisticians and statistical users.

《Annual Review of Statistics and Its Application》是一本年度回顾期刊，旨在向统计学家和统计用户介绍统计学领域的主要方法学进展及其应用的计算工具。

Annu. Rev. Stat. Appl.

Functional Data Analysis

An overview of functional data analysis 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).

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数学	1
数学, 数学跨学科应用	1
数学, 统计学与概率论	1

Functional Data Analysis

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	1