Posterior regret Γ-minimax estimation in a normal model with asymmetric loss function

Agata Boratyńska

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Displaying similar documents to “Posterior regret Γ-minimax estimation in a normal model with asymmetric loss function”

Robust Bayesian estimation with asymmetric loss function

Agata Boratyńska (2002)

Applicationes Mathematicae

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The problem of robust Bayesian estimation in some models with an asymmetric loss function (LINEX) is considered. Some uncertainty about the prior is assumed by introducing two classes of priors. The most robust and conditional Γ-minimax estimators are constructed. The situations when those estimators coincide are presented.

Two-point priors and minimax estimation of a bounded parameter under convex loss

Agata Boratyńska (2005)

Applicationes Mathematicae

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The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.

An improved Bayes empirical Bayes estimator.

Karunamuni, R.J., Prasad, N.G.N. (2003)

International Journal of Mathematics and Mathematical Sciences

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A review of the results on the Stein approach for estimators improvement.

Vassiliy G. Voinov, Mikhail S. Nikulin (1995)

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Since 1956, a large number of papers have been devoted to Stein's technique of obtaining improved estimators of parameters, for several statistical models. We give a brief review of these papers, emphasizing those aspects which are interesting from the point of view of the theory of unbiased estimation.

Unbiased risk estimation method for covariance estimation

Hélène Lescornel, Jean-Michel Loubes, Claudie Chabriac (2014)

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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.

Minimax estimation of a cumulative distribution function for a special loss function

S Trybuła (1991)

Applicationes Mathematicae

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An alternative analysis of variance.

Nicholas T. Longford (2008)

SORT

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The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.

On empirical Bayes estimation of multivariate regression coefficient.

Karunamuni, R.J., Wei, L. (2006)

International Journal of Mathematics and Mathematical Sciences

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Bayesian estimation of AR(1) models with uniform innovations

Hocine Fellag, Karima Nouali (2005)

Discussiones Mathematicae Probability and Statistics

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The first-order autoregressive model with uniform innovations is considered. In this paper, we propose a family of BAYES estimators based on a class of prior distributions. We obtain estimators of the parameter which perform better than the maximum likelihood estimator.

A sufficient condition for admissibility in linear estimation

Czesław Stępniak (1988)

Aplikace matematiky

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It was recently shown that all estimators which are locally best in the relative interior of the parameter set, together with their limits constitute a complete class in linear estimation, both unbiased and biased. However, not all these limits are admissible. A sufficient condition for admissibility of a limit was given by the author (1986) for the case of unbiased estimation in a linear model with the natural parameter space. This paper extends this result to the general linear model...