  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. They are both examples of "functional data", which have become a
prevailing 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 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, such as
time warping, manifold learning, and dynamic modeling with empirical
differential equations. The paper concludes with a brief discussion of future
directions.
