Methodology and convergence rates for functional linear regression

摘要: In functional linear regression, the slope ``parameter'' is a function. Therefore, in nonparametric context, it determined by an infinite number of unknowns. Its estimation involves solving ill-posed problem and has points contact with range methodologies, including statistical smoothing deconvolution. The standard approach to estimating function based explicitly on principal components analysis and, consequently, spectral decomposition terms eigenvalues eigenfunctions. We discuss this detail show that certain circumstances, optimal convergence rates are achieved PCA technique. An alternative quadratic regularisation suggested shown have advantages from some view.