Functional data analysis

Summary

Functional data analysis is the branch of statistics in which each observation is a whole function, such as a curve, a surface or an image. The functions are modelled as random elements of an infinite-dimensional space, usually the Hilbert space $L^2$ of square-integrable functions. Its basic tools are the mean function, the covariance operator and functional principal component analysis, which rests on the Karhunen–Loève theorem. It also has regression models in which the predictor or the response is a function.