Abstract.
We consider nonparametric estimation of a multivariate function and its partial derivatives at a fixed point when the Riesz transform of the function is observed in Gaussian white noise. We assume that the unknown function belongs to some Sobolev class and construct an estimation procedure which achieves the best asymptotic minimax risk when the smoothness of the function is unknown.
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Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/6-2 and Rolf Nevanlinna Institute.
Mathematics Subject Classification (2000): 62G05, 62G20
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Klemelä, J., Tsybakov, A. Exact constants for pointwise adaptive estimation under the Riesz transform. Probab. Theory Relat. Fields 129, 441–467 (2004). https://doi.org/10.1007/s00440-004-0348-9
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DOI: https://doi.org/10.1007/s00440-004-0348-9
Key words or phrases:
- Adaptive curve estimation
- Bandwidth selection
- Deconvolution
- Exact constants in nonparametric smoothing
- Gaussian white noise
- Inverse problems
- Kernel estimation
- Minimax risk