Asymptotically minimax Bayes predictive densities
نویسندگان
چکیده
fθ log (fθ/f̂) is used to examine various ways of choosing prior distributions; the principal type of choice studied is minimax. We seek asymptotically least favorable predictive densities for which the corresponding asymptotic risk is minimax. A result resembling Stein’s paradox for estimating normal means by the maximum likelihood holds for the uniform prior in the multivariate location family case: when the dimensionality of the model is at least three, the Jeffreys prior is minimax, though inadmissible. The Jeffreys prior is both admissible and minimax for oneand two-dimensional location problems.
منابع مشابه
Improved Minimax Predictive Densities under Kullback – Leibler Loss
Let X|μ∼Np(μ,vxI ) and Y |μ∼Np(μ,vyI ) be independent p-dimensional multivariate normal vectors with common unknown mean μ. Based on only observing X = x, we consider the problem of obtaining a predictive density p̂(y|x) for Y that is close to p(y|μ) as measured by expected Kullback–Leibler loss. A natural procedure for this problem is the (formal) Bayes predictive density p̂U(y|x) under the unif...
متن کاملImproved Minimax Prediction Under Kullback-Leibler Loss
Let X | μ ∼ Np(μ, vxI) and Y | μ ∼ Np(μ, vyI) be independent p-dimensional multivariate normal vectors with common unknown mean μ, and let p(x|μ) and p(y |μ) denote the conditional densities of X and Y . Based on only observing X = x, we consider the problem of obtaining a predictive distribution p̂(y |x) for Y that is close to p(y |μ) as measured by Kullback-Leibler loss. The natural straw man ...
متن کاملAsymptotically minimax regret for exponential families
We study the problem of data compression, gambling and prediction of a sequence x = x1x2...xn from a certain alphabet X , in terms of regret and redundancy with respect to a general exponential family. In particular, we evaluate the regret of the Bayes mixture density and show that it asymptotically achieves their minimax values when variants of Jeffreys prior are used. Keywords— universal codi...
متن کاملMinimax Estimator of a Lower Bounded Parameter of a Discrete Distribution under a Squared Log Error Loss Function
The problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function....
متن کاملAsymptotically minimax regret by Bayes mixtures - Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
We study the problem of data compression, gambling and prediction of a sequence zn = z1z2 ... z, from a certain alphabet X , in terms of regret [4] and redundancy with respect to a general exponential family, a general smooth family, and also Markov sources. In particular, we show that variants of Jeffreys mixture asymptotically achieve their minimax values. These results are generalizations of...
متن کامل