Secondly, under the square loss, we construct the asymptotically optimal and admissible empirical Bayes estimator of the mean for normal distribution, theconvergence rate O(n~(-1)) is also obtained.
In the paper the family of normal distribution{N(μ,σ~2)| -∞<μ<+∞,σ~2>0} is considered. The linear empirical Bayes estimators of μ,σ~2 and θ=(μ,σ~2)′ are constructed by the method of Robbins and Tao Bo.
对于正态分布族{N(μ,σ~2)|-∞<μ<+∞,σ~2>0},本文利用Robbins,Tao Bo 的思想,分别构造了μ,σ~2,θ=(μ,σ~2)′的线性经验 Bayes估计,我们不但在一定条件下讨论了这些估计的 a.
n this paper,the empirical Bayes estimate of the parameter of uniform distribution family is introduced and for the absolute error loss its asymptotically optimal property is proved with respect to the prior distribution family(1).
A basic problem of Empirical Bayes estimate in theoretical research is to look for suitable Empirical Bayes estimation and to prove it to be asymptotic optimal.
In this thesis, the Empirical Bayes estimations and multiple Empirical Bayes estimations of success probability theta of Boinomial distribution were given out by moment estimate when theta followed different priors, and the superiority of these estimations was simply discussed. With analog computation some of these estimates was found to be superior to the linear Empirical Bayes estimate given out by Robbins and these estimats were proved to be strong consistent and asymptotic optimal(a.o.)
The asymptotically optimal empirical bayes estimation in multiple linear regression model
Empirical Bayes estimation of the parameter vector θ=(β',σ2)' in a multiple linear regression modelY=Xβ+ε is considered, where β is the vector of regression coefficient, ε∽N(0,σI with σ2 unknown.
Individual Prior Information in a Physiological Model of 2H8-Toluene Kinetics: An Empirical Bayes Estimation Strategy
Empirical Bayes estimation of gene-specific effects in micro-array research
Empirical Bayes estimation of gene-specific effects in micro-array research
In [1] the empirical Bayes estimator of the parameter vector of normal distribution family was introduced, and for the loss function (1) its asymptotically optimal property was proved with respect to the prior distribution family (2).
In this paper the thought on the uniform convergence of an empirical Bayes estimator or linear empirical Bayes (l.e.B.) estimator is advanced.
In this setting, we consider PRL reliability measures based on two estimators of the correct category-the empirical Bayes estimator and an estimator based on the judges' consensus choice.
The results show the best behaviour of Empirical Bayes estimator (EB).
It is established that the empirical Bayes estimator is inadmissible and the improved estimators are also derived.
The simulation result shows as improvement of the Bayesian estimate over the empirical Bayes estimate in some situations.
The cause for the biased estimates appears to be related to the conditioning on uninformative and uncertain empirical Bayes estimate of interindividual random effects during the estimation, in conjunction with the normality assumption.