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@article{1655218, author = {Kraus, David and Stefanucci, Marco}, article_location = {Amsterdam}, article_number = {OCT 2020}, doi = {http://dx.doi.org/10.1016/j.spl.2020.108813}, keywords = {Functional data; Partial observation; Reconstruction; Reproducing kernel Hilbert space; Ridge regularization}, language = {eng}, issn = {0167-7152}, journal = {Statistics and Probability Letters}, title = {Ridge reconstruction of partially observed functional data is asymptotically optimal}, url = {https://doi.org/10.1016/j.spl.2020.108813}, volume = {165}, year = {2020} }
TY - JOUR ID - 1655218 AU - Kraus, David - Stefanucci, Marco PY - 2020 TI - Ridge reconstruction of partially observed functional data is asymptotically optimal JF - Statistics and Probability Letters VL - 165 IS - OCT 2020 SP - 1-5 EP - 1-5 PB - Elsevier SN - 01677152 KW - Functional data KW - Partial observation KW - Reconstruction KW - Reproducing kernel Hilbert space KW - Ridge regularization UR - https://doi.org/10.1016/j.spl.2020.108813 L2 - https://doi.org/10.1016/j.spl.2020.108813 N2 - 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. ER -
KRAUS, David a Marco STEFANUCCI. Ridge reconstruction of partially observed functional data is asymptotically optimal. \textit{Statistics and Probability Letters}. Amsterdam: Elsevier, 2020, roč.~165, OCT 2020, s.~1-5. ISSN~0167-7152. Dostupné z: https://dx.doi.org/10.1016/j.spl.2020.108813.
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