Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators

10.4 Factor analysis

In this section, we explore the problem of factor analysis under the same conditions as Section 10.3. For that purpose, we consider the signal-plus-noise model given by

10.25

for . Here , and are all zero mean, valued processes with covariance kernels , and . The signal process, , is assumed to be uncorrelated with the noise process . With this latter specification model (10.25) can be viewed as the natural extension of the mva factor model (1.21) to continuous time.

Following along the lines of our factor analysis development in Section 1.1, our first step should be canonical ...