1 Fourth and Fifth Order Efficiency : Fisher Information

Loss of (Fisher) information, whose concept was de ned by Fisher, is one of important measures of asymptotic e ciency. Based on Fisher information, this paper studies fourth and fth order asymptotic e ciency of estimators in a curved exponential family of distributions with a structural parameter vector. In particular, we show that the bias-corrected MLE with a certain bias correction factor is fourth and fth order e cient in a class of Fisher consistent estimators bias-corrected similarly.