When I reading the
Functional Data Analysis
Writen by J.O. Ramsay B.W. Silverman.
At page 229, the author use the formula below to explain what is functional linear model,
$Prec_{mg}(t)=\mu(t)+\alpha_g(t)+\varepsilon_{mg}(t)$
And then the author said, $\varepsilon_{mg}(t)$ is the residual function.
I was confused that if we can use a function to specify the uncertainty, there should be no error then. I can not understand this point. Who can help me to explain this?