Stochastic expansions of unbiased estimators for the case of one-parameter exponential family

Asymptotic and stochastic expansions are obtained for all unbiased estimators which can be constructed from a repeated sample of independent identically distributed random variables having one and the same distribution from a one-parameter exponential family. A comparison is conducted of expansions of unbiased estimators with those of maximum likelihood estimators. A stochastic expansion is obtained for an unbiased estimator of the variance of an unbiased estimator.