Displaying similar documents to “Minimax and Bayes estimation when the loss function is unknown”

Some investigations in minimax estimation theory

Stanisław Trybuła

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1. IntroductionThough the theory of minimax estimation was originated about thirty five years ago (see [7], [8], [9], [23]), there are still many unsolved problems in this area. Several papers have been devoted to statistical games in which the set of a priori distributions of the parameter was suitably restricted ([2], [10], [13]). Recently, special attention was paid to the problem of admissibility ([24], [3], [11], [12]).This paper is devoted to the problem of determining minimax...

Γ-minimax sequential estimation for Markov-additive processes

Ryszard Magiera (2001)

Applicationes Mathematicae

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The problem of estimating unknown parameters of Markov-additive processes from data observed up to a random stopping time is considered. To the problem of estimation, the intermediate approach between the Bayes and the minimax principle is applied in which it is assumed that a vague prior information on the distribution of the unknown parameters is available. The loss in estimating is assumed to consist of the error of estimation (defined by a weighted squared loss function) as well...

On a trivariate Poisson distribution

Sotirios Loukas, Evgenia H. Papageorgiou (1991)

Applications of Mathematics

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A four parameter trivariate Poisson distribution is considered. Recurrences for the probabilities and the partial derivatives of the probabilities with respect to the parameters are derived. Solutions of the maximum likelihood equations are obtaired and the determinant of their asymptotic covariance matrix is given. Applications of the maximum likelihood estimation technique to simulated data sets are also examined.

The Bayes sequential estimation of a normal mean from delayed observations

Alicja Jokiel-Rokita (2006)

Applicationes Mathematicae

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The problem of estimating the mean of a normal distribution is considered in the special case when the data arrive at random times. Certain classes of Bayes sequential estimation procedures are derived under LINEX and reflected normal loss function and with the observation cost determined by a function of the stopping time and the number of observations up to this time.

Bayes sequential estimation procedures for exponential-type processes

Ryszard Magiera (1994)

Applicationes Mathematicae

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The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.