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analysis applications approximation assume assumption asymptotic Bayes estimator Bayes risk Bayesian Berger Blackwell sufficient bootstrap Brownian Chapter classical concave function condition consider Corollary Csorgo Decision Theory defined denote density Department of Mathematics Department of Statistics Dudewicz empirical Bayes estimator equation equivariant estimators estimation problem example exists exponential distribution exponential family finite frequentist Germany Prof Ghosh given GS r.v. Hence holds implies inequality integral Lemma likelihood function linear loss function Markov operator Math mean squared error measurable space minimax multivariate nonparametric normal obtain Oldenbourg Verlag optimal p-value paper prior distribution probability measure Probn processes Prof Dr random variables rates of convergence regression respect result risk function sample satisfies scale parameters Section sequence Springer squared error statistical decision statistical experiment stochastic strictly GS symmetric tests Theorem 3.1 U. S. A. Prof uniform uniformly University vector weak Markov kernels