Minimax estimation and prediction for random variables with bounded sum
S. Trybuła (1987)
Applicationes Mathematicae
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S. Trybuła (1987)
Applicationes Mathematicae
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Shayle R. Searle (1995)
Metrika
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P. Mukhopadhyay, V.R. Padmawar (1985)
Metrika
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František Štulajter (1976)
Kybernetika
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Paul Chiou, Chien-Pai Eon (1996)
Metrika
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R. Zmyślony (1976)
Applicationes Mathematicae
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S. Trybuła (1991)
Applicationes Mathematicae
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Maciej Wilczyński (2003)
Applicationes Mathematicae
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Let Y be a random vector taking its values in a measurable space and let z be a vector-valued function defined on that space. We consider gamma minimax estimation of the unknown expected value p of the random vector z(Y). We assume a weighted squared error loss function.
Doron Sonsino (2000)
ESAIM: Probability and Statistics
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J. Bartoszewicz (1977)
Applicationes Mathematicae
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Beniamin Goldys (1985)
Banach Center Publications
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Saralees Nadarajah (2007)
Applicationes Mathematicae
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Data that are proportions arise most frequently in biomedical research. In this paper, the exact distributions of R = X + Y and W = X/(X+Y) and the corresponding moment properties are derived when X and Y are proportions and arise from the most flexible bivariate beta distribution known to date. The associated estimation procedures are developed. Finally, two medical data sets are used to illustrate possible applications.
Solev, V.N., Haghighi, F. (2004)
Journal of Mathematical Sciences (New York)
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H. Truszczyńska (1987)
Applicationes Mathematicae
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Jelena Bulatović, Alobodanka Janjić (1979)
Publications de l'Institut Mathématique
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Hélène Lescornel, Jean-Michel Loubes, Claudie Chabriac (2014)
ESAIM: Probability and Statistics
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We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.