  We consider the functional linear regression model with a scalar response and
a Hilbert space-valued predictor, a well-known ill-posed inverse problem. We
propose a new formulation of the functional partial least-squares (PLS)
estimator related to the conjugate gradient method. We shall show that the
estimator achieves the (nearly) optimal convergence rate on a class of
ellipsoids and we introduce an early stopping rule which adapts to the unknown
degree of ill-posedness. Some theoretical and simulation comparison between the
estimator and the principal component regression estimator is provided.
