Takeuchi [37], Takeuchi and Akahira [38] and Pfanzagl [27] among others proved that any rst-order ecient estimators are second-order ecient. Many authors e.g., Ghosh [15], have conjectured that any third-order ecient estimators are fourth-order ecient. Based on concentration probability of estimators about a true parameter, this paper gives a positive answer to the conjecture in a curved expone...
