Numerical methods for linear minimax estimation

Norbert Gaffke; Berthold Heiligers

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 1, page 51-62
  • ISSN: 1509-9423

Abstract

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We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior distribution.

How to cite

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Norbert Gaffke, and Berthold Heiligers. "Numerical methods for linear minimax estimation." Discussiones Mathematicae Probability and Statistics 20.1 (2000): 51-62. <http://eudml.org/doc/287612>.

@article{NorbertGaffke2000,
abstract = {We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior distribution.},
author = {Norbert Gaffke, Berthold Heiligers},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Bayes estimation; duality; linear model; L-optimality; mean squared error; minimax estimation; non-smooth optimization; parameter restrictions; p-mean; quasi Newton method; parametric restrictions},
language = {eng},
number = {1},
pages = {51-62},
title = {Numerical methods for linear minimax estimation},
url = {http://eudml.org/doc/287612},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Norbert Gaffke
AU - Berthold Heiligers
TI - Numerical methods for linear minimax estimation
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 1
SP - 51
EP - 62
AB - We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior distribution.
LA - eng
KW - Bayes estimation; duality; linear model; L-optimality; mean squared error; minimax estimation; non-smooth optimization; parameter restrictions; p-mean; quasi Newton method; parametric restrictions
UR - http://eudml.org/doc/287612
ER -

References

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  13. [13] J. Lauterbach, Zur Berechnung approximativer Minimax-Schätzer im linearen Regressionsmodell, Dissertationthesis, Universität Hannover, Germany 1989 (in German). 
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