论文标题
在乘法测量误差下的密度估计的光谱截止正规化
Spectral cut-off regularisation for density estimation under multiplicative measurement errors
论文作者
论文摘要
我们研究了基于I.I.D的R+支持的未知密度F的非参数估计。带有乘法测量误差的样品。提出的完全数据驱动的过程基于密度F的梅林变换的估计，这是通过频谱截止和数据驱动模型选择的梅林转换倒数的正则化，以应对即将到来的偏见差异权衡。我们介绍并讨论了进一步的Mellin-Sobolev空间，这些空间表征了未知密度F的规律性，其Mellin Transform的衰减。此外，我们在数据驱动的密度估计器的Mellin-sobolev空间上显示了最小值，因此其适应性。
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.
