文章基本信息

标题：Anisotropic de-noising in functional deconvolution model with dimension-free convergence rates
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作者：Rida Benhaddou ; Marianna Pensky ; Dominique Picard 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：1686-1715
DOI：10.1214/13-EJS820
语种：English
出版社：Institute of Mathematical Statistics
摘要：In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^{2}$-risk when $f$ belongs to a Besov ball of mixed smoothness and demonstrate that the wavelet estimator is adaptive and asymptotically near-optimal within a logarithmic factor, in a wide range of Besov balls. We prove in particular that choosing this type of mixed smoothness leads to rates of convergence which are free of the “curse of dimensionality” and, hence, are higher than usual convergence rates when $r$ is large.