Cavalier, L. Nonparametric statistical inverse problems. (English) Zbl 1137.62323 Inverse Probl. 24, No. 3, Article ID 034004, 19 p. (2008). 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. Cited in 71 Documents MSC: 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference Keywords:regularization methods PDFBibTeX XMLCite \textit{L. Cavalier}, Inverse Probl. 24, No. 3, Article ID 034004, 19 p. (2008; Zbl 1137.62323) Full Text: DOI Link