  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 early stopping sequential
discrepancy principle and the balancing principle, both theoretically and
numerically.
