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...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
July 2022
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| In: |
Journal of multivariate analysis
Year: 2022, Volume: 190, Pages: 1-18 |
| ISSN: | 1095-7243 |
| DOI: | 10.1016/j.jmva.2022.104990 |
| Online Access: | 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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| Author Notes: | Sergio Brenner Miguel |
| Summary: | 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. |
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| Item Description: | Available online 16 March 2022 Gesehen am 13.06.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7243 |
| DOI: | 10.1016/j.jmva.2022.104990 |