# Risk hull method for spectral regularization in linear statistical inverse problems

ESAIM: Probability and Statistics (2010)

- Volume: 14, page 409-434
- ISSN: 1292-8100

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topMarteau, Clément. "Risk hull method for spectral regularization in linear statistical inverse problems." ESAIM: Probability and Statistics 14 (2010): 409-434. <http://eudml.org/doc/250852>.

@article{Marteau2010,

abstract = {
We consider in this paper the statistical linear inverse problem Y = Af + ϵξ where A denotes a compact operator, ϵ a noise level and ξ a stochastic noise. The unknown function f has to be recovered from the indirect measurement Y. We are interested in the following approach: given a family of estimators, we want to select the best possible one. In this context, the unbiased risk estimation (URE) method is rather popular. Nevertheless, it is also very unstable. Recently, Cavalier and Golubev (2006) introduced the risk hull minimization (RHM) method. It significantly improves the performances of the standard URE procedure. However, it only concerns projection rules. Using recent developments on ordered processes, we prove in this paper that it can be extended to a large class of linear estimators.
},

author = {Marteau, Clément},

journal = {ESAIM: Probability and Statistics},

keywords = {Inverse problems; oracle inequality; ordered process; risk hull and Tikhonov estimation; inverse problems},

language = {eng},

month = {12},

pages = {409-434},

publisher = {EDP Sciences},

title = {Risk hull method for spectral regularization in linear statistical inverse problems},

url = {http://eudml.org/doc/250852},

volume = {14},

year = {2010},

}

TY - JOUR

AU - Marteau, Clément

TI - Risk hull method for spectral regularization in linear statistical inverse problems

JO - ESAIM: Probability and Statistics

DA - 2010/12//

PB - EDP Sciences

VL - 14

SP - 409

EP - 434

AB -
We consider in this paper the statistical linear inverse problem Y = Af + ϵξ where A denotes a compact operator, ϵ a noise level and ξ a stochastic noise. The unknown function f has to be recovered from the indirect measurement Y. We are interested in the following approach: given a family of estimators, we want to select the best possible one. In this context, the unbiased risk estimation (URE) method is rather popular. Nevertheless, it is also very unstable. Recently, Cavalier and Golubev (2006) introduced the risk hull minimization (RHM) method. It significantly improves the performances of the standard URE procedure. However, it only concerns projection rules. Using recent developments on ordered processes, we prove in this paper that it can be extended to a large class of linear estimators.

LA - eng

KW - Inverse problems; oracle inequality; ordered process; risk hull and Tikhonov estimation; inverse problems

UR - http://eudml.org/doc/250852

ER -

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