Linex Loss Of Parameter Estimation And Its Properties

The Bayes method was put forward but not received too much attention at the beginning, then through the continuous development and perfection by itself to form a theory, and had become an important branch of the statistical theorem, which had a wide application. This paper at first introduced the development of the Bayes statistics and the decision, and also the relevant basic knowledge; Then used the Bayes thought to discuss the estimation of the parameter, and obtained some good conclusions, this article was mainly divided into two parts:The first part of this article was the third chapter, in this chapter, combined the Statistical decision with the Bayes method,got the sufficient conditions that the minimax estimation of parameter’s function was equivalent to its Bayes estimation, under the loss function for LINEX, in the prior distribution of two parameters, Given in the form of theory and its proof. And then proved that the minimax estimation of the poisson distribution parameters and its Bayes estimation meet that conditions are equivalent.The second part at first gave the conditions how the Bayes posterior criterion of the parameter and its Bayes estimation were equivalent, the next to discuss the admissible of the Bayes estimation of the exponential distribution parameters in the prior distribution for Γ, under the LINEX loss function, and then extended to some parameters form as mln(1+a/(n+β), and got some preliminary admissible conclusions about their Bayes estimation.