ABSTRACT
This chapter presents a unified theory to show the asymptotic efficiency of the maximum likelihood estimators (and some other estimators based on the likelihood functions) in any parametric models where the asymptotic behavior of the log-likelihood function can be fully analyzed. The theory is based on the concept of local asymptotic normality (LAN) of sequences of statistical experiments. The main results are Hajek-Inagaki's convolution theorem and Hajek-Le Cam's asymptotic minimax theorem, both of which were established in the early 1970s. The asymptotic representation theorem studied in the previous chapter plays an important role in the process of applying the LAN theory with the help of Le Cam's third lemma.
