Third order efficiency implies fourth order efficiency: A resolution of the conjecture of J. K. Ghosh

Masafumi Akahira1
1Institute of Mathematics, University of Tsukuba, Ibaraki, Japan

Tóm tắt

Từ khóa


Tài liệu tham khảo

Akahira, M. (1986). The structure of asymptotic deficiency of estimators, Queen's Papers in Pure and Appl. Math., 75, Queen's University Press, Kingston, Canada.

Akahira, M. (1992). Higher order asymptotics and asymptotic deficiency of estimators, Selecta Statistica Canadiana, 8, 1?36.

Akahira, M. and Takeuchi, K. (1976). On the second order asymptotic efficiency of estimators in multiparameter cases, Rep. Univ. Electro-Comm., 26, 261?269.

Akahira, M. and Takeuchi, K. (1981). Asymptotic efficiency of statistical estimators: concepts and higher order efficiency, Lecture Notes in Statist., 7, Springer, New York.

Akahira, M. and Takeuchi, K. (1989). Third order asymptotic efficiency of the sequential maximum likelihood estimation procedure, Sequential Anal., 8, 333?359.

Amari, S. (1985). Differential-geometrical methods in statistics, Lecture Notes in Statist., 28, Springer, Berlin.

Bhattacharya, R. N. and Ghosh, J. K. (1978). Validity of the formal Edgeworth expansion, Ann. Statist., 6, 434?451.

Bickel, P. J., Chibisov, D. M. and vanZwet, W. R. (1981). On efficiency of first and second order, Internat. Statist. Rev., 49, 169?175.

Fisher, R. A. (1925). Theory of statistical estimation, Proc. Camb. Phil. Soc., 22, 700?725.

Ghosh, J. K. (1994). Higher order asymptotics, NSF-CBMS Regional Conference Series Probability and Statistics, 4, Institute of Mathematical Statistics, Hayward, California.

Ghosh, J. K. and Sinha, B. K. (1982). Third order efficiency of the MLE-a counterexample, Calcutta Statist. Assoc. Bull., 31, 151?158.

Ghosh, J. K. and Subramanyam, K. (1974). Second order efficiency of maximum likelihood estimators, Sankhy? Ser. A, 36, 325?358.

Kano, Y. (1994). More higher order efficiency: Concentration probability (unpublished).

Kendall, M. G. and Stuart, A. (1969). The Advanced Theory of Statistics, Vol. 1, Charles Griffin, London.

Pfanzagl, J. (1979). First order efficiency implies second order efficiency. Contributions to Statistics: Jaroslav Hájek Memorial Volume (ed. J.Jure?ková), 167?196, Academia, Prague.

Pfanzagl, J. and Wefelmeyer, W. (1985). Asymptotic expansions for general statistical models, Lecture Notes in Statist., 31, Springer, Berlin.

Rao, C. R. (1961). Asymptotic efficiency and limiting information, Proc. Fourth Berkeley Symp. on Math. Statist. Prob., Vol. 1, 531?545.

Takeuchi, K. and Akahira, M. (1976). On the second order asymptotic efficiencies of estimators, Proceedings of the Third Japan-USSR Symposium on Probability Theory (eds. G.Maruyama and J. V.Prokhorov), 604?638, Lecture Notes in Math., 550, Springer, Berlin.