Status: Bibliographieeintrag
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| Verfasst von: | Rademacher, Daniel C. [VerfasserIn]  |
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| | Krebs, Johannes [VerfasserIn] |
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| | Sachs, Rainer von [VerfasserIn] |
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| Titel: | Statistical inference for wavelet curve estimators of symmetric positive definite matrices |
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| Verf.angabe: | Daniel Rademacher, Johannes Krebs, Rainer von Sachs |
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| E-Jahr: | 2024 |
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| Jahr: | July 2024 |
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| Umfang: | 33 S. |
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| Fussnoten: | Available online 9 January 2024 ; Gesehen am 22.04.2024 |
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| Titel Quelle: | Enthalten in: Journal of statistical planning and inference |
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| Ort Quelle: | Amsterdam : North-Holland Publ. Co., 1977 |
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| Jahr Quelle: | 2024 |
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| Band/Heft Quelle: | 231(2024), Artikel-ID 106140, Seite 1-33 |
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| ISSN Quelle: | 0378-3758 |
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| Abstract: | In this paper we treat statistical inference for a wavelet estimator of curves of symmetric positive definite (SPD) using the log-Euclidean distance. This estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation (AI) and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups. The core of our work is the proposition of confidence sets for our AI wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality of this estimator, including explicit expressions of its asymptotic variance. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes. |
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| DOI: | doi:10.1016/j.jspi.2023.106140 |
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| URL: | Bitte beachten Sie: Dies ist ein Bibliographieeintrag. Ein Volltextzugriff für Mitglieder der Universität besteht hier nur, falls für die entsprechende Zeitschrift/den entsprechenden Sammelband ein Abonnement besteht oder es sich um einen OpenAccess-Titel handelt.
Volltext: https://doi.org/10.1016/j.jspi.2023.106140 |
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| | Volltext: https://www.sciencedirect.com/science/article/pii/S037837582300109X |
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| | DOI: https://doi.org/10.1016/j.jspi.2023.106140 |
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| Datenträger: | Online-Ressource |
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| Sprache: | eng |
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| Sach-SW: | AI refinement |
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| | Asymptotic normality |
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| | Covariance matrices |
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| | log-Euclidean manifold |
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| | Matrix-valued curves |
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| | Second generation wavelets |
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| K10plus-PPN: | 1886516804 |
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| Verknüpfungen: | → Zeitschrift |
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Statistical inference for wavelet curve estimators of symmetric positive definite matrices / Rademacher, Daniel C. [VerfasserIn]; July 2024 (Online-Ressource)
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