Presmoothing in Functional Linear Regression

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Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study (2017, methodology): “First, the conditional mean square error of β̂S was derived by Hall and Hosseini-Nasab (2006) and Ferraty et al. (2012), and is given by: E [∥∥∥β − β̂S∥∥∥2 |χ1, . . . , χn] = σ2e n kn∑ k=1 1 âk + ∥∥∥R̂kn∥∥∥2 , (13) where R̂kn = ∑∞ k=kn+1 〈 β, ψ̂k 〉 ψ̂k.”