Anisotropic spectral cut-off estimation under multiplicative measurement errors

• Verfasst von: Brenner Miguel, Sergio Filipe [VerfasserIn]
• Titel: Anisotropic spectral cut-off estimation under multiplicative measurement errors
• Verf.angabe: Sergio Brenner Miguel
• E-Jahr: 2022
• Jahr: July 2022
• Umfang: 18 S.
• Fussnoten: Available online 16 March 2022 ; Gesehen am 13.06.2022
• Titel Quelle: Enthalten in: Journal of multivariate analysis
• Ort Quelle: Orlando, Fla. : Acad. Press, 1971
• Jahr Quelle: 2022
• Band/Heft Quelle: 190(2022), Artikel-ID 104990, Seite 1-18
• ISSN Quelle: 1095-7243
• DOI: doi:10.1016/j.jmva.2022.104990
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Adaptation
• Sach-SW: Anisotropic density estimation
• Sach-SW: Anisotropic Mellin-Sobolev spaces
• Sach-SW: Inverse problem
• Sach-SW: Mellin transform
• Sach-SW: Minimax theory
• Sach-SW: Multiplicative measurement errors
• K10plus-PPN: 1806863057

Abstract

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.