The E Bayesian Estimation And The Hierarchical Bayesian Estimation Of The Parameter

There are two kinds of great thoughts in mathematical statistics—Bayesian and Classical thoughts.The argument between the two great thougut constituted the important characteristic of the modern development mathematical statistic.The Bayes thougut considered that we obtain the sample is to adjust the prior knowledge of the estimated parameter.In mathematical that is to say,after obtaining the sampleχ,we may obtain the conditional distribution H(dλ|χ)when X=χ.In the traditional Bayesian estimation,the prior distribution is known,but sometimes we can't obtain the precise priori distribution,therefore there are some new methods of Bayesian estimation, such as the E Bayesian estimation and hierarchical estimation.This paper has studied the Bayesian estimation,E E Bayesian estimation and hierarchical estimation of the scale parameterλunder the square loss function and the entropy loss function,as well as the comparison between them.