Singular wavelets on a finite interval
Nonparametric methods are used in complex cases where model information is insufficient. A new method of nonparametric approximation, the singular wavelet method, is developed. The method includes a numerical algorithm based on the summation of a recurrent sequence of functions. The introduction exp...
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| Format: | Article |
| Language: | Russian |
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The United Institute of Informatics Problems of the National Academy of Sciences of Belarus
2018-12-01
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| Series: | Informatika |
| Subjects: | |
| Online Access: | https://inf.grid.by/jour/article/view/253 |
| _version_ | 1797877335556358144 |
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| author | V. M. Romanchak |
| author_facet | V. M. Romanchak |
| author_sort | V. M. Romanchak |
| collection | DOAJ |
| description | Nonparametric methods are used in complex cases where model information is insufficient. A new method of nonparametric approximation, the singular wavelet method, is developed. The method includes a numerical algorithm based on the summation of a recurrent sequence of functions. The introduction explains the idea of the singular wavelet method to combine the theory of wavelets with kernel regression estimation of the Nadaraya - Watson type. This integration is realized by regularizing the wavelet transform. Usually kernel estimation is are considered as an example of nonparametric estimation. However, one parameter - the blur parameter - is still present in the traditional kernel regression algorithm. In the approximation by the method of singular value wavelet, the summation of kernel estimation of the type Nadaraya - Watson using the blur parameter takes place. In the main part of the work, the variant of wavelet transform regularization for the finite interval is considered. Theorems that formulate the properties of a wavelet transform with a singular wavelet are proved, an algorithm for approximating a function defined on a finite interval by a sequence of wavelet transforms is proposed. |
| first_indexed | 2024-04-10T02:15:32Z |
| format | Article |
| id | doaj.art-c956868e23f34568a18b95a6615b5558 |
| institution | Directory Open Access Journal |
| issn | 1816-0301 |
| language | Russian |
| last_indexed | 2024-04-10T02:15:32Z |
| publishDate | 2018-12-01 |
| publisher | The United Institute of Informatics Problems of the National Academy of Sciences of Belarus |
| record_format | Article |
| series | Informatika |
| spelling | doaj.art-c956868e23f34568a18b95a6615b55582023-03-13T08:32:20ZrusThe United Institute of Informatics Problems of the National Academy of Sciences of BelarusInformatika1816-03012018-12-011543949435Singular wavelets on a finite intervalV. M. Romanchak0Belarusian National Technical UniversityNonparametric methods are used in complex cases where model information is insufficient. A new method of nonparametric approximation, the singular wavelet method, is developed. The method includes a numerical algorithm based on the summation of a recurrent sequence of functions. The introduction explains the idea of the singular wavelet method to combine the theory of wavelets with kernel regression estimation of the Nadaraya - Watson type. This integration is realized by regularizing the wavelet transform. Usually kernel estimation is are considered as an example of nonparametric estimation. However, one parameter - the blur parameter - is still present in the traditional kernel regression algorithm. In the approximation by the method of singular value wavelet, the summation of kernel estimation of the type Nadaraya - Watson using the blur parameter takes place. In the main part of the work, the variant of wavelet transform regularization for the finite interval is considered. Theorems that formulate the properties of a wavelet transform with a singular wavelet are proved, an algorithm for approximating a function defined on a finite interval by a sequence of wavelet transforms is proposed.https://inf.grid.by/jour/article/view/253wavelet transformthe parzen - rosenblatt window methodnonparametric estimatornadaraya -watson kernel regression |
| spellingShingle | V. M. Romanchak Singular wavelets on a finite interval Informatika wavelet transform the parzen - rosenblatt window method nonparametric estimator nadaraya -watson kernel regression |
| title | Singular wavelets on a finite interval |
| title_full | Singular wavelets on a finite interval |
| title_fullStr | Singular wavelets on a finite interval |
| title_full_unstemmed | Singular wavelets on a finite interval |
| title_short | Singular wavelets on a finite interval |
| title_sort | singular wavelets on a finite interval |
| topic | wavelet transform the parzen - rosenblatt window method nonparametric estimator nadaraya -watson kernel regression |
| url | https://inf.grid.by/jour/article/view/253 |
| work_keys_str_mv | AT vmromanchak singularwaveletsonafiniteinterval |