关于Cramer-Rao下界的推广

Some Improvements of the Cramer-Rao Lower Bound

从Cramer-Rao信息不等式出发,详细地证明了当T(x)是g(θ)的无偏估计且满足T(x)-g(θ)是1 L/Lθ,1L2/Lθ2,L的线性函数时,T(x)的方差可以达到Bhattacharyya下界,并给出实例.从而推广了C-R下界.

We based on the Cramer-Rao inequality and elaborately prove the fact that when T（X） is the unbiased estimator of the function g（θ） and T（X） -g（θ） is the linear function of L^（1）/L, L^（2）/L,…,then the variance of T（X） may dose not satisfy the C-R lower bound, but it is also an optimum estimator of g（θ）. Moreover, it reach Bhattacharyya lower bound.