caa a22 4500 477063187 CHVBK 20180405111406.0 cr unu---uuuuu 170330e19960601xx s 000 0 eng 10.1007/BF00054796 doi (NATIONALLICENCE)springer-10.1007/BF00054796 Akahira Masafumi Institute of Mathematics, University of Tsukuba, 305, Ibaraki, Japan aut Third order efficiency implies fourth order efficiency: A resolution of the conjecture of J. K. Ghosh [Elektronische Daten] [Masafumi Akahira] Under suitable regularity conditions, it is shown that a third order asymptotically efficient estimator is fourth order asymptotically efficient in some class of estimators in the sense that the estimator has the most concentration probability in any symmetric interval around the true parameter up to the fourth order in the class. This is a resolution of the conjecture by Ghosh (1994, Higher Order Asymptotics, Institute of Mathematical Statistics, Hayward, California). It is also shown that the bias-adjusted maximum likelihood estimator is fourth order asymptotically efficient in the class. The Institute of Statistical Mathematics, 1996 Asymptotically median unbiasedness nationallicence fourth order asymptotically symmetric efficiency nationallicence concentration probability nationallicence asymptotic cumulants nationallicence Edgeworth expansion nationallicence maximum likelihood estimator nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/2(1996-06-01), 365-380 0020-3157 48:2<365 1996 48 10463 https://doi.org/10.1007/BF00054796 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00054796 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Akahira Masafumi Institute of Mathematics, University of Tsukuba, 305, Ibaraki, Japan aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/2(1996-06-01), 365-380 0020-3157 48:2<365 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer