Course 11 Functional Data Analysis

Functional Data Analysis (FDA) is a statistical framework for analyzing data where each observation is a function, curve, or surface observed over a continuum, such as time or space. Unlike traditional multivariate methods that deal with finite-dimensional vectors, FDA handles infinite-dimensional data, making it suitable for studying complex patterns and continuous processes. It provides tools for smoothing, modeling, and interpreting functional data, often leveraging basis expansions like splines or Fourier series. Applications of FDA span diverse fields, including medicine, finance, environmental science, and engineering, where data such as growth curves, financial trends, and temperature records naturally arise as functions.

https://en.wikipedia.org/wiki/Donsker_classes https://en.wikipedia.org/wiki/Donsker%27s_theorem