Functional Data Analysis: An Introduction and Recent Developments

Area of Science:

• Statistics
• Data Science

Background:

• Functional data analysis (FDA) extends statistical methods to curves, images, and functions.
• High-dimensional nature of functional data presents unique analytical challenges.

Purpose of the Study:

• Introduce fundamental concepts and techniques in FDA.
• Describe software implementations and recent advancements in the field.
• Demonstrate FDA methods with practical examples.

Main Methods:

• Descriptive statistics, outlier detection, and smoothing for functional data.
• Functional principal component analysis (FPCA) and functional regression.
• Classification, clustering, and machine learning approaches for functional data.

Main Results:

• Comprehensive overview of core FDA techniques.
• Discussion of amplitude and phase variation, and statistical inference.
• Application of methods using R software on human motion data.

Conclusions:

• FDA methods are broadly applicable across scientific disciplines like medicine and neuroscience.
• The paper provides accessible code and data for hands-on learning.
• Sparse functional data methods are highlighted for longitudinal data analysis.