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Anisotropic spectral cut-off estimation under multiplicative measurement errors

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  • Brenner Miguel, Sergio

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.

Suggested Citation

  • Brenner Miguel, Sergio, 2022. "Anisotropic spectral cut-off estimation under multiplicative measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000288
    DOI: 10.1016/j.jmva.2022.104990
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    References listed on IDEAS

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    1. Elodie Brunel & Fabienne Comte & Valentine Genon-Catalot, 2016. "Nonparametric density and survival function estimation in the multiplicative censoring model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 570-590, September.
    2. F. Comte & C. Dion, 2016. "Nonparametric estimation in a multiplicative censoring model with symmetric noise," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 768-801, October.
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