  We analyse the properties of the Principal Fitted Components (PFC) algorithm
proposed by Cook. We derive theoretical properties of the resulting estimators,
including sufficient conditions under which they are $\sqrt{n}$-consistent, and
explain some of the simulation results given in Cook's paper. We use techniques
from random matrix theory and perturbation theory. We argue that, under Cook's
model at least, the PFC algorithm should outperform the Principal Components
algorithm.
