关于有效估计的一点讨论

A Little Discussion about Effective Estimation

一致最小方差无偏估计是所有无偏估计中方差最小的,有效估计是满足特定条件的无偏估计中方差最小的。通过2个例题说明了有效估计未必存在,即C-R下界未必能够达到,若C-R不等式的条件不成立,无偏估计的方差可能小于C-R下界。

The uniform minimum variance unbiased estimation is the least variance among all unbiased estimations and the effective estimation is the least variance among all unbiased estimations satisfying certain conditions.This paper illustrates through examples that effective estimation may not exist,that is,C-R lower bound may not be reached.If the condition of c-r inequality is not established,the variance of unbiased estimation may be less than C-R lower bound.