A Variational View on Statistical Multiscale Estimation
2022 | journal article. A publication with affiliation to the University of Göttingen.
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- Authors
- Haltmeier, Markus; Li, Housen ; Munk, Axel
- Abstract
- We present a unifying view on various statistical estimation techniques including penalization, variational, and thresholding methods. These estimators are analyzed in the context of statistical linear inverse problems including nonparametric and change point regression, and high-dimensional linear models as examples. Our approach reveals many seemingly unrelated estimation schemes as special instances of a general class of variational multiscale estimators, called MIND (multiscale Nemirovskii–Dantzig). These estimators result from minimizing certain regularization functionals under convex constraints that can be seen as multiple statistical tests for local hypotheses. For computational purposes, we recast MIND in terms of simpler unconstraint optimization problems via Lagrangian penalization as well as Fenchel duality. Performance of several MINDs is demonstrated on numerical examples.
- Issue Date
- 2022
- Journal
- Annual Review of Statistics and Its Application
- Project
- SFB 1456: Mathematik des Experiments: Die Herausforderung indirekter Messungen in den Naturwissenschaften
SFB 1456 | Cluster B | B04: Collective dynamics of ion channels: statistical modeling and analysis
EXC 2067: Multiscale Bioimaging
SFB 1456 | Cluster A | A04: Dynamics of cytoskeletal networks: From geometric structure to cell mechanics - Working Group
- RG Li
RG Munk - ISSN
- 2326-8298
- eISSN
- 2326-831X
- Language
- English