Volume 57, pp. 35-56, 2022.

A probabilistic oracle inequality and quantification of uncertainty of a modified discrepancy principle for statistical inverse problems

Tim Jahn


In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy principle. We provide probabilistic oracle inequalities together with quantification of uncertainty for general linear problems. Moreover, we compare the new method to existing ones, namely the early stopping sequential discrepancy principle and the balancing principle, both theoretically and numerically.

Full Text (PDF) [338 KB], BibTeX

Key words

statistical inverse problems, non-Bayesian approach, discrepancy principle, oracle inequality, early stopping

AMS subject classifications

65J20, 62G99

< Back