# Invariance and R-ε criterion.

• Volume: 1, Issue: 2, page 37-45
• ISSN: 0213-8190

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## Abstract

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The R-ε criterion is considered as a generalization of the minimax criterion, in a decision problem with Θ = {θ1, ..., θn}, and its relation with the invariance is studied. If a decision problem is invariant under a finite group G, it is known, from the minimax point of view that, for any rule δ, there exists an invariant rule δ' which is either preferred or equivalent to δ. The question raised in this paper is: given that the minimax ordering is a particular case of R-ε ordering, is it possible to extend this property to the R-ε criterion? And, if the answer is negative, is it possible to give a sufficient and necessary condition for R-ε orderings with this property? A complete answer is given to this problem; it is proved that the property does not hold true for any R-ε ordering that does not coincide with the minimax ordering.

## How to cite

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Horra, Julián de la. "Invariance and R-ε criterion.." Trabajos de Estadística 1.2 (1986): 37-45. <http://eudml.org/doc/40480>.

@article{Horra1986,
abstract = {The R-ε criterion is considered as a generalization of the minimax criterion, in a decision problem with Θ = \{θ1, ..., θn\}, and its relation with the invariance is studied. If a decision problem is invariant under a finite group G, it is known, from the minimax point of view that, for any rule δ, there exists an invariant rule δ' which is either preferred or equivalent to δ. The question raised in this paper is: given that the minimax ordering is a particular case of R-ε ordering, is it possible to extend this property to the R-ε criterion? And, if the answer is negative, is it possible to give a sufficient and necessary condition for R-ε orderings with this property? A complete answer is given to this problem; it is proved that the property does not hold true for any R-ε ordering that does not coincide with the minimax ordering. },
author = {Horra, Julián de la},
keywords = {Criterio minimax; Decisión estadística; Invariancia; R-epsilon criterion; generalization of the minimax criterion; invariance; minimax ordering},
language = {eng},
number = {2},
pages = {37-45},
title = {Invariance and R-ε criterion.},
url = {http://eudml.org/doc/40480},
volume = {1},
year = {1986},
}

TY - JOUR
AU - Horra, Julián de la
TI - Invariance and R-ε criterion.
PY - 1986
VL - 1
IS - 2
SP - 37
EP - 45
AB - The R-ε criterion is considered as a generalization of the minimax criterion, in a decision problem with Θ = {θ1, ..., θn}, and its relation with the invariance is studied. If a decision problem is invariant under a finite group G, it is known, from the minimax point of view that, for any rule δ, there exists an invariant rule δ' which is either preferred or equivalent to δ. The question raised in this paper is: given that the minimax ordering is a particular case of R-ε ordering, is it possible to extend this property to the R-ε criterion? And, if the answer is negative, is it possible to give a sufficient and necessary condition for R-ε orderings with this property? A complete answer is given to this problem; it is proved that the property does not hold true for any R-ε ordering that does not coincide with the minimax ordering.
LA - eng
KW - Criterio minimax; Decisión estadística; Invariancia; R-epsilon criterion; generalization of the minimax criterion; invariance; minimax ordering
UR - http://eudml.org/doc/40480
ER -

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