Functional data structures

Abstract

Statistics is concerned with obtaining information from observations X ₁, X ₂, …, X _N . The X _n can be scalars, vectors or other objects. For example, each X _n can be a satellite image, in some spectral bandwidth, of a particular region of the Earth taken at time n. Functional Data Analysis (FDA) is concerned with observations which are viewed as functions defined over some set T. A satellite image processed to show surface temperature can be viewed as a function X defined on a subset T of a sphere, X(t) being the temperature at location t. The value X _n (t) is then the temperature at location t at time n. Clearly, due to finite resolution, the values of X _n are available only at a finite grid of points, but the temperature does exist at every location, so it is natural to view X _n as a function defined over the whole set T.