On exact and optimal recovering of missing values for sequences
The paper studies recoverability of missing values for sequences in a pathwise setting without probabilistic assumptions. This setting is oriented on a situation where the underlying sequence is considered as a sole sequence rather than a member of an ensemble with known statistical properties. Suff...
| Main Author: | |
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| Format: | Journal Article |
| Published: |
Elsevier BV
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/19145 |
| _version_ | 1848749949373644800 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| author_sort | Dokuchaev, Nikolai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The paper studies recoverability of missing values for sequences in a pathwise setting without probabilistic assumptions. This setting is oriented on a situation where the underlying sequence is considered as a sole sequence rather than a member of an ensemble with known statistical properties. Sufficient conditions of recoverability are obtained; it is shown that sequences are recoverable if there is a certain degree of degeneracy of the Z-transforms. We found that, in some cases, this degree can be measured as the number of the derivatives of Z-transform vanishing at a point. For processes with non-degenerate Z-transform, an optimal recovering based on the projection on a set of recoverable sequences is suggested. Some robustness of the solution with respect to noise contamination and truncation is established. |
| first_indexed | 2025-11-14T07:29:04Z |
| format | Journal Article |
| id | curtin-20.500.11937-19145 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:29:04Z |
| publishDate | 2017 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-191452025-03-27T05:08:05Z On exact and optimal recovering of missing values for sequences Dokuchaev, Nikolai The paper studies recoverability of missing values for sequences in a pathwise setting without probabilistic assumptions. This setting is oriented on a situation where the underlying sequence is considered as a sole sequence rather than a member of an ensemble with known statistical properties. Sufficient conditions of recoverability are obtained; it is shown that sequences are recoverable if there is a certain degree of degeneracy of the Z-transforms. We found that, in some cases, this degree can be measured as the number of the derivatives of Z-transform vanishing at a point. For processes with non-degenerate Z-transform, an optimal recovering based on the projection on a set of recoverable sequences is suggested. Some robustness of the solution with respect to noise contamination and truncation is established. 2017 Journal Article http://hdl.handle.net/20.500.11937/19145 10.1016/j.sigpro.2016.12.024 Elsevier BV fulltext |
| spellingShingle | Dokuchaev, Nikolai On exact and optimal recovering of missing values for sequences |
| title | On exact and optimal recovering of missing values for sequences |
| title_full | On exact and optimal recovering of missing values for sequences |
| title_fullStr | On exact and optimal recovering of missing values for sequences |
| title_full_unstemmed | On exact and optimal recovering of missing values for sequences |
| title_short | On exact and optimal recovering of missing values for sequences |
| title_sort | on exact and optimal recovering of missing values for sequences |
| url | http://hdl.handle.net/20.500.11937/19145 |