  Functional data analysis (FDA) is a statistical framework that allows for the
analysis of curves, images, or functions on higher dimensional domains. The
goals of FDA, such as descriptive analyses, classification, and regression, are
generally the same as for statistical analyses of scalar-valued or multivariate
data, but FDA brings additional challenges due to the high- and infinite
dimensionality of observations and parameters, respectively. This paper
provides an introduction to FDA, including a description of the most common
statistical analysis techniques, their respective software implementations, and
some recent developments in the field. The paper covers fundamental concepts
such as descriptives and outliers, smoothing, amplitude and phase variation,
and functional principal component analysis. It also discusses functional
regression, statistical inference with functional data, functional
classification and clustering, and machine learning approaches for functional
data analysis. The methods discussed in this paper are widely applicable in
fields such as medicine, biophysics, neuroscience, and chemistry, and are
increasingly relevant due to the widespread use of technologies that allow for
the collection of functional data. Sparse functional data methods are also
relevant for longitudinal data analysis. All presented methods are demonstrated
using available software in R by analyzing a data set on human motion and motor
control. To facilitate the understanding of the methods, their implementation,
and hands-on application, the code for these practical examples is made
available on Github: https://github.com/davidruegamer/FDA_tutorial .
