Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms
Iain M. Johnstone, K. Brenda Macgibbon (1993)
Annales de l'I.H.P. Probabilités et statistiques
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Iain M. Johnstone, K. Brenda Macgibbon (1993)
Annales de l'I.H.P. Probabilités et statistiques
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Mikhail Ermakov (2008)
ESAIM: Probability and Statistics
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We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function where and is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...
Agata Boratyńska (2002)
Applicationes Mathematicae
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The problem of posterior regret Γ-minimax estimation under LINEX loss function is considered. A general form of posterior regret Γ-minimax estimators is presented and it is applied to a normal model with two classes of priors. A situation when the posterior regret Γ-minimax estimator, the most stable estimator and the conditional Γ-minimax estimator coincide is presented.
Peter Hall, Byeong U. Park, Berwin A. Turlach (2002)
Annales de l'I.H.P. Probabilités et statistiques
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José M. Bernardo (2007)
SORT
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Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations,...
Karunamuni, R.J., Prasad, N.G.N. (2003)
International Journal of Mathematics and Mathematical Sciences
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Jean Bretagnolle, Jan Mielniczuk (1989)
Annales de l'I.H.P. Probabilités et statistiques
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S Trybuła (1991)
Applicationes Mathematicae
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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.