Supersmooth functional data analysis and PCA-preprocessing
Moritz Jirak and Alexander Meister
Nowadays, in many applications data is recorded sequentially over time at high resolution exhibiting certain degrees of dependence and smoothness. In such cases it is reasonable to model data as functions. Nonparametric regression estimation and classification for functional data is studied when the underlying target functions are supersmooth. Contrarily to usual nonparametric problems in functional data analysis, algebraic convergence rates of the statistical procedures appear to be achievable. The goal is to derive computationally efficient statistical procedures, largely being unaffected by heavy tails and dependencies, and to prove their asymptotic optimality. The information theoretic complexity is governed by a delicate interplay of metric entropies and algebraic properties of the eigenvalues and principal components of the covariance operators of the functional data.