  Functional principal component regression (PCR) can fail to provide good
prediction if the response is highly correlated with some excluded functional
principal component(s). This situation is common since the construction of
functional principal components never involves the response. Aiming at this
shortcoming, we develop functional continuum regression (CR). The framework of
functional CR includes, as special cases, both functional PCR and functional
partial least squares (PLS). Functional CR is expected to own a better accuracy
than functional PCR and functional PLS both in estimation and prediction;
evidence for this is provided through simulation and numerical case studies.
Also, we demonstrate the consistency of estimators given by functional CR.
