Arbeitspapier
The asymptotic minimax risk for the estimation of constrained binomial and multinomial probabilities
In this note we present a direct and simple approach to obtain bounds on the asymptotic minimax risk for the estimation of restrained binominal and multinominal proportions. Quadratic, normalized quadratic and entropy loss are considered and it is demonstrated that in all cases linear estimators are asymptotically minimax optimal. For the quadratic loss function the asymptotic minimax rsik does not change unless a neighborhood of the point 1/2 is excluded by the restrictions on the parameter space. For the two other loss functions the asymptotic minimax risks remain unchanged if additional knowledge about the location of the unknown probability of success is imposed. The results are also extended to the problem of minimax estimation of a vector of contrained multinominal propabilities.
- Language
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Englisch
- Bibliographic citation
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Series: Technical Report ; No. 2004,18
- Subject
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binominal distribution
multinominal distribution
entropy loss
quadratic loss
constrained parameter space
least favourable distribution
- Event
-
Geistige Schöpfung
- (who)
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Braess, Dietrich
Dette, Holger
- Event
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Veröffentlichung
- (who)
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Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
- (where)
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Dortmund
- (when)
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2004
- Handle
- Last update
- 10.03.2025, 11:44 AM CET
Data provider
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ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Braess, Dietrich
- Dette, Holger
- Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
Time of origin
- 2004
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