On the Attainment of the Cramer-Rao Lower Bound

R. A. Wijsman

doi:10.1214/aos/1176342419

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Home > Journals > Ann. Statist. > Volume 1 > Issue 3 > Article

May, 1973 On the Attainment of the Cramer-Rao Lower Bound

R. A. Wijsman

Ann. Statist. 1(3): 538-542 (May, 1973). DOI: 10.1214/aos/1176342419

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Abstract

A rigorous proof is given of the often stated fact that if the variance of an unbiased estimator of a function of a real parameter attains the Cramer-Rao lower bound then the family of distributions must be a one-parameter exponential family.