线性指数分布参数的经验贝叶斯估计

Empirical Bayes estimation of linear exponential distribution parameters

对线性指数分布在平方损失下获得了参数的贝叶斯估计,并构造了相应的经验贝叶斯估计,证明了所提出的经验贝叶斯估计是渐近最优的且有收敛速度O(n-q),其中q=(s-1)(λs-1)/[s(2s+1)],1/2<λ<1-1/(2s),s≥2是一给定的整数.

Empirical Bayes estimation was derived under square loss function and empirical Bayes estimations of the parameter were constructed for linear exponential distribution. It is shown that the proposed empirical Bayes estimations are asymptotically optimal with convergence rates O （n^-q ）, where, q=（s-1）（λs-1）/[s（2s＋1.）], and 1/2〈λ〈1-1/（2s）, s≥2 is a given integer.