To develop new FPCA’s based on P-spline smoothing with B-spline basis for noisy data. These smoothed FPCA’s will be applied to solve the multicollinearity and lack of smoothness problems that affect estimation of the functional parameter in functional regression models as well as linear models and functional logit models, amongst others. Alternatively, and in order to solve the same problem, different forms of penalised estimation of the functional PLS regression will be introduced.