Spectral cut-off regularisation for density estimation under multiplicative measurement errors
We study the non-parametric estimation of an unknown density f with support on R+ 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, a regularisation of the inverse of the Mel...
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| Hauptverfasser: | , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2021
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| In: |
Electronic journal of statistics
Year: 2021, Jahrgang: 15, Heft: 1, Pages: 3551-3573 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/21-EJS1870 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1214/21-EJS1870 Verlag, lizenzpflichtig, Volltext: https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=DynamicDOIArticle&SrcApp=WOS&KeyAID=10.1214%2F21-EJS1870&DestApp=DOI&SrcAppSID=D1XQZgTychBOaRFzNdb&SrcJTitle=ELECTRONIC+JOURNAL+OF+STATISTICS&DestDOIRegistrantName=Institute+of+Mathematical+Statistics 
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| Verfasserangaben: | Sergio Brenner Miguel, Fabienne Comte, Jan Johannes |
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| 520 | |a We study the non-parametric estimation of an unknown density f with support on R+ 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, a regularisation of the inverse of the Mellin transform by a spectral cut-off and a data-driven model selection in order to deal with the upcoming bias-variance trade-off. We introduce and discuss further Mellin-Sobolev spaces which characterize 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 data-driven density estimator and hence its adaptivity. | ||
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| 650 | 4 | |a Mellin-Sobolev space | |
| 650 | 4 | |a minimax theory | |
| 650 | 4 | |a multiplicative measurement errors | |
| 650 | 4 | |a nonparametric density | |
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