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2020 Smoothed residual stopping for statistical inverse problems via truncated SVD estimation
Bernhard Stankewitz
Electron. J. Statist. 14(2): 3396-3428 (2020). DOI: 10.1214/20-EJS1747


This work examines under what circumstances adaptivity for truncated SVD estimation can be achieved by an early stopping rule based on the smoothed residuals $\|(AA^{\top })^{\alpha /2}(Y-A\widehat{\mu }^{(m)})\|^{2}$. Lower and upper bounds for the risk are derived, which show that moderate smoothing of the residuals can be used to adapt over classes of signals with varying smoothness, while oversmoothing yields suboptimal convergence rates. The range of smoothness classes for which adaptation is possible can be controlled via $\alpha $. The theoretical results are illustrated by Monte-Carlo simulations.


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Bernhard Stankewitz. "Smoothed residual stopping for statistical inverse problems via truncated SVD estimation." Electron. J. Statist. 14 (2) 3396 - 3428, 2020.


Received: 1 September 2019; Published: 2020
First available in Project Euclid: 21 September 2020

zbMATH: 07270267
MathSciNet: MR4152147
Digital Object Identifier: 10.1214/20-EJS1747

Primary: 62G05 , 65J20

Keywords: adaptive estimation , discrepancy principle , early stopping , linear inverse problems , Oracle inequalities , spectral cut-off , weighed residuals


Vol.14 • No. 2 • 2020
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