Publication details

Ridge reconstruction of partially observed functional data is asymptotically optimal



Year of publication 2020
Type Article in Periodical
Magazine / Source Statistics and Probability Letters
MU Faculty or unit

Faculty of Science

Keywords Functional data; Partial observation; Reconstruction; Reproducing kernel Hilbert space; Ridge regularization
Description When functional data are observed on parts of the domain, it is of interest to recover the missing parts of curves. Kraus (2015) proposed a linear reconstruction method based on ridge regularization. Kneip and Liebl (2019) argue that an assumption under which Kraus (2015) established the consistency of the ridge method is too restrictive and propose a principal component reconstruction method that they prove to be asymptotically optimal. In this note we relax the restrictive assumption that the true best linear reconstruction operator is Hilbert–Schmidt and prove that the ridge method achieves asymptotic optimality under essentially no assumptions. The result is illustrated in a simulation study.
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