| Presentation | 2005-04-22 Minimum-Variance Pseudo-Unbiased Low-Rank Estimation : A Generalization of Marquardt's Estimator for Ill-Conditioned Inverse Problems Jamal ELBADRAOUI, Isao YAMADA, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | This paper presents a novel low-rank linear statistical estimator named minimum-variance pseudo-unbiased low-rank estimator for applications to ill-conditioned linear inverse problems. Based on a simple fact : 'any low-rank estimator can not be a (uniformly) unbiased estimator', we introduce pseudo-unbiased low-rank estimator, as a novel class of low-rank estimators. We also define the minimum-variance pseudo-unbiased low-rank estimator which minimizes the variance of estimate among all pseudo-unbiased low-rank estimators. The pseudo-unbiased low-rank estimator and the minimum-variance pseudo-unbiased low-rank estimator are respectively natural generalizations of the unbiased estimator and the minimum-variance unbiased estimator (i.e., Gauss-Markov estimator) in the statistical estimation theory. The main theorem presents an algebraic structure of the minimum-variance pseudo-unbiased low-rank estimator in terms of the singular value decomposition of the model matrix in the linear statistical model. By this theorem, it is revealed that the minimum-variance pseudo-unbiased low-rank estimator is a nontrivial generalization of the Marquardt's low-rank estimator (Marquardt 1970). |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Ill-conditioned inverse problem / Low-rank estimator / Marquardt's rank-reduction estimator / Pseudo-unbiased low-rank estimator / Minimum-variance pseudo-unbiased low-rank estimator |
| Paper # | SIP2005-6,IE2005-6 |
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| Conference Information | |
| Committee | IE |
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| Conference Date | 2005/4/15(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Image Engineering (IE) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Minimum-Variance Pseudo-Unbiased Low-Rank Estimation : A Generalization of Marquardt's Estimator for Ill-Conditioned Inverse Problems |
| Sub Title (in English) | |
| Keyword(1) | Ill-conditioned inverse problem |
| Keyword(2) | Low-rank estimator |
| Keyword(3) | Marquardt's rank-reduction estimator |
| Keyword(4) | Pseudo-unbiased low-rank estimator |
| Keyword(5) | Minimum-variance pseudo-unbiased low-rank estimator |
| 1st Author's Name | Jamal ELBADRAOUI |
| 1st Author's Affiliation | Dept. of Communications & Integrated Systems, Tokyo Institute of Technology() |
| 2nd Author's Name | Isao YAMADA |
| 2nd Author's Affiliation | Dept. of Communications & Integrated Systems, Tokyo Institute of Technology |
| Date | 2005-04-22 |
| Paper # | SIP2005-6,IE2005-6 |
| Volume (vol) | vol.105 |
| Number (no) | 30 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |