Anisotropic spectral cut-off estimation under multiplicative measurement errors
We study the non-parametric estimation of an unknown density f with support on R+d based on an i.i.d. sample with multiplicative measurement errors. The proposed fully-data driven procedure is based on the estimation of the Mellin transform of the density f and a regularization of the inverse of Mel...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
July 2022
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| In: |
Journal of multivariate analysis
Year: 2022, Jahrgang: 190, Pages: 1-18 |
| ISSN: | 1095-7243 |
| DOI: | 10.1016/j.jmva.2022.104990 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jmva.2022.104990 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0047259X22000288 
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| Verfasserangaben: | Sergio Brenner Miguel |
MARC
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| 520 | |a We study the non-parametric estimation of an unknown density f with support on R+d based on an i.i.d. sample with multiplicative measurement errors. The proposed fully-data driven procedure is based on the estimation of the Mellin transform of the density f and a regularization of the inverse of Mellin transform by a spectral cut-off. The bias-variance tradeoff for estimating f is optimized with a data-driven anisotropic choice of the cutoff parameter. In order to discuss the bias term, we consider the Mellin-Sobolev spaces which define the regularity of the unknown density f through the decay of its Mellin transform. Additionally, we show minimax-optimality over Mellin-Sobolev spaces of the spectral cut-off density estimator. | ||
| 650 | 4 | |a Adaptation | |
| 650 | 4 | |a Anisotropic density estimation | |
| 650 | 4 | |a Anisotropic Mellin-Sobolev spaces | |
| 650 | 4 | |a Inverse problem | |
| 650 | 4 | |a Mellin transform | |
| 650 | 4 | |a Minimax theory | |
| 650 | 4 | |a Multiplicative measurement errors | |
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