【摘要】 <正> 具有共同支撑的单参数分布族{pθ,θ∈},R,若它满足一定的正则条件,Cramér-Rao给出了可估函数g(θ)的所有无偏估计的方差的下界函数,即著名的C-R不等式。Fend和Wijsman指出:在这些正则条件下,g(θ)的无偏估计T(x)处处达到C-R下界的充要条件,是{pθ,θ∈}为指数族,对某σ-有限测度μ(x)的密度形为更多还原

【Abstract】 For the natural exponential family {f(x, θ)=exp[T(x)θ+Ψ(θ)], θ ∈} where is an open interval, we use m=E_θT(x), instead of θ, as parameter. By the orthogonal expansion method, some properties about the Fisher information matrix I_n(m) are given and the variance function of UMVUE of estimable g (m), when the variance is finite everywhere, is proved to be equal to either the Bhattacharyyà lower bound B_n(m) with finite(?)n, or the limit of B_n(m) when n→∞.更多还原