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Nonparametric statistical inverse problems. (English) Zbl 1137.62323

Summary: We explain some basic theoretical issues regarding nonparametric statistics applied to inverse problems. Simple examples are used to present classical concepts such as the white noise model, risk estimation, minimax risk, model selection and optimal rates of convergence, as well as more recent concepts such as adaptive estimation, oracle inequalities, modern model selection methods, Stein’s unbiased risk estimation and the very recent risk hull method.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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