Displaying similar documents to “Note on minimax solutions of statistical decision problems”

Optimal alternative robustness in Bayesian Decision Theory.

Fabrizio Ruggeri, Jacinto Martín, David Ríos Insua (2003)

RACSAM

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In Martin et al (2003), we suggested an approach to general robustness studies in Bayesian Decision Theory and Inference, based on ε-contamination neighborhoods. In this note, we generalise the results considering neighborhoods based on norms, specifically, the supremum norm for utilities and the total variation norm for probability distributions. We provide tools to detect changes in preferences between alternatives under perturbations of the prior and/or the utility and the most sensitive...

On the foundations of statistics and decision theory.

José M. Bernardo, Javier Girón (1983)

Trabajos de Estadística e Investigación Operativa

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An elementary axiomatic foundation for decision theory is presented at a general enough level to cover standard applications of Bayesian methods. The intuitive meaning of both axioms and results is stressed. It is argued that statistical inference is a particular decision problem to which the axiomatic argument fully applies.

Alternative definitions of conditional possibilistic measures

Ivan Kramosil (1998)

Kybernetika

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The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information...

Possibilistic alternatives of elementary notions and relations of the theory of belief functions

Ivan Kramosil (2001)

Kybernetika

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The elementary notions and relations of the so called Dempster–Shafer theory, introducing belief functions as the basic numerical characteristic of uncertainty, are modified to the case when probabilistic measures and basic probability assignments are substituted by possibilistic measures and basic possibilistic assignments. It is shown that there exists a high degree of formal similarity between the probabilistic and the possibilistic approaches including the role of the possibilistic...

Invariance and R-ε criterion.

Julián de la Horra (1986)

Trabajos de Estadística

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The R-ε criterion is considered as a generalization of the minimax criterion, in a decision problem with Θ = {θ, ..., θ}, 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...

Robust inference in probability under vague information.

Giuliana Regoli (1996)

Mathware and Soft Computing

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Vague information can be represented as comparison of previsions or comparison of probabilities, and a robust analysis can be done, in order to make inference about some quantity of interest and to measure the imprecision of the answers. In particular, in some decision problems the answer can be unique.