Empirical Bayes Estimation Of The Parameter For Geometric Distribution And It's Optimum

The thought of empirical Bayes method was first came from Von Mises(1942), and then it was formally put forward by Robbins in 1955. The domestic and foreign scholars did a lot of foundation work. They selected some representative density functions and suitable loss functions to estimate the parameters that were contained in these functions, and they discuss-ed the asymptotic optimality of these estimates. The geometric distribution is one of the basic discrete probability distributions and it is closely related many other important distributions. So studying the geometric distribution is very meaningful.In this paper, empirical Bayes estimation of the parameter theta for geometric distributi-on is discussed. Firstly, we introduce the common method, and give out empirical Bayes estimation under the square loss function when conjugate distribution is the prior distribution, then its asymptotic optimality is discussed with the different method. Secondly, taking the un-iform distribution in (λ,1) as the prior distribution when conjugate distribution beta(a,b) is unavailable,0≤λ≤θ≤1. Empirical Bayes estimation is given out under the square loss function and this estimate is proved to be strong consistent and asymptotic optimal.