 Anisotropic spectral cut-off estimation under multiplicative measurement errorsSergio Brenner Miguel Journal of Multivariate Analysis, 2022, vol. 190, issue C 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. Keywords: Adaptation; Anisotropic density estimation; Anisotropic Mellin–Sobolev spaces; Inverse problem; Mellin transform; Minimax theory; Multiplicative measurement errors (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000288 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2022.104990 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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