The paper provides a historical and expository review of the classical work on first order asymptotic efficiency. The following topics are discussed: Fisher’s and LeCam’s inequality, Cramer-Rao inequality, Hájek-Inagaki convolution theorem, local asymptotic minimaxity, asymptotic normality of posteriors, approximate Bayes character of maximum likelihood estimates, and limiting experiments. The author states that this is the first part of a two part article.
It should be noted, as the author also mentions, that partial reviews of asymptotic efficiency have already appeared by J. Hájek [Proc. 6th Berkeley Sympos. math. Statist. Probab., Univ. Calif. 1970, 1, 175- 194 (1972; Zbl 0281.62010)], G. Roussas [Contiguity of probability measures. Some applications in statistics. (1972; Zbl 0265.60003)], I. Ibragimov and R. Z. Khas’minskij [Statistical estimation. Asymptotic Theory. (1981; Zbl 0467.62026)], and E. L. Lehmann [Theory of point estimation. (1983; Zbl 0522.62020)].