Principal Modes of Variation for Processes With Continuous Sample Curves

Abstract

Analysis of a process with continuous sample curves can be carried out in a manner similar to principal components analysis of vector processes. By appropriate definition of a best linear model in the continuous case, we show that principal modes of variation consist of eigenfunctions of the process covariance function C(s, t). Procedures for estimation of these eigenfunctions from a finite sample of observed curves are given, and results are compared with principal components analysis of the same data.

KEY WORDS:

• Continuous process
• Karhunen–Loève expansion
• Principal components
• Linear mode