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arXiv · 0710.1045

Regularization independent of the noise level: an analysis of quasi-optimality

Frank Bauer·Markus Reiss
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Abstract

The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators and we prove that the quasi-optimality criterion determines estimators which are rate-optimal {\em on average}. Its practical performance is illustrated with a calibration problem from mathematical finance.

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Frank Bauer, Markus Reiss. 2007-10-04. Regularization independent of the noise level: an analysis of quasi-optimality. https://doi.org/10.1088/0266-5611%2F24%2F5%2F055009

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