The development of the higher order asymptotic theory of statistical estimation is described and the structure of the theory is clarified. From the viewpoint of concentration probability of estimators around a true parameter, the asymptotic efficiency of estimators is discussed up to the higher order. In particular, the phenomenon “third order efficiency implies fourth order efficiency” is derived and applied to the bias-adjusted maximum likelihood estimator and the bias-adjusted generalized Bayes estimator. The results bring us the essence of higher order asymptotics.