In this paper,the necessary and sufficient conditions for a function of the parameterin a one-parameter natural exponential family(NEF)to have an unbiased estimator withfinite variance are obtained.The recursive formu...In this paper,the necessary and sufficient conditions for a function of the parameterin a one-parameter natural exponential family(NEF)to have an unbiased estimator withfinite variance are obtained.The recursive formulae of the Fisher information matrices of anyorder for a one-parameter NEF and a one-parameter regular exponential family(REF)arederived respectively.The expression of the UMVUE for an estimable function of the parameterin a one-parameter NEF or a one-parameter REF is given.展开更多
基金This work is supported by the Academic Fund of Academia Sinica
文摘In this paper,the necessary and sufficient conditions for a function of the parameterin a one-parameter natural exponential family(NEF)to have an unbiased estimator withfinite variance are obtained.The recursive formulae of the Fisher information matrices of anyorder for a one-parameter NEF and a one-parameter regular exponential family(REF)arederived respectively.The expression of the UMVUE for an estimable function of the parameterin a one-parameter NEF or a one-parameter REF is given.