On optimal prediction of missing functional data with memory
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912098629451776 |
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| author | Ilmonen, Pauliina Shafik, Nourhan Sottinen, Tommi Van Bever, Germain Viitasaari, Lauri |
| author_facet | Ilmonen, Pauliina Shafik, Nourhan Sottinen, Tommi Van Bever, Germain Viitasaari, Lauri |
| contents | This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the $L^2$-optimal reconstruction of the missing parts. These functions are obtained as solutions of explicit integral equations. In the discrete case, approximations of the solutions provide consistent expressions of all missing values of the processes. Rates of convergence of these approximations, under extra assumptions on the transformation function, are provided. In the case of Gaussian processes with a parametric covariance structure, the estimation can be conducted separately for each function, and yields nonlinear solutions in presence of memory. Simulated examples show that the proposed reconstruction indeed fares better than the conventional interpolation methods in various situations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09925 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On optimal prediction of missing functional data with memory Ilmonen, Pauliina Shafik, Nourhan Sottinen, Tommi Van Bever, Germain Viitasaari, Lauri Statistics Theory Probability 62R10, 60G15, 60G25 This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the $L^2$-optimal reconstruction of the missing parts. These functions are obtained as solutions of explicit integral equations. In the discrete case, approximations of the solutions provide consistent expressions of all missing values of the processes. Rates of convergence of these approximations, under extra assumptions on the transformation function, are provided. In the case of Gaussian processes with a parametric covariance structure, the estimation can be conducted separately for each function, and yields nonlinear solutions in presence of memory. Simulated examples show that the proposed reconstruction indeed fares better than the conventional interpolation methods in various situations. |
| title | On optimal prediction of missing functional data with memory |
| topic | Statistics Theory Probability 62R10, 60G15, 60G25 |
| url | https://arxiv.org/abs/2208.09925 |