Bulletin of the American Mathematical Society

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Book Information:

Authors: I. A. Ibragimov and R. Z. Has′minskii
Title: Statistical estimation, asymptotic theory
Additional book information: Applications of Mathematics, vol. 16, Springer-Verlag, New York, 1981, vii + 403 pp., $42.00. ISBN 0-3879-0523-5.

Author: J. Pfanzagl
Title: Contributions to a general asymptotic statistical theory
Additional book information: (with the assistance of W. Wefelmeyer), Lecture Notes in Statistics, vol. 13, Springer-Verlag, New York, 1982, vii + 315 pp., $16.80. ISBN 0-3879-0776-9.

Masafumi Akahira and Kei Takeuchi, Asymptotic efficiency of statistical estimators: concepts and higher order asymptotic efficiency, Lecture Notes in Statistics, vol. 7, Springer-Verlag, New York-Berlin, 1981. MR 617375

Patrice Assouad, Deux remarques sur l’estimation, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 23, 1021–1024 (French, with English summary). MR 777600

Ishwar V. Basawa and B. L. S. Prakasa Rao, Statistical inference for stochastic processes, Probability and Mathematical Statistics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. MR 586053

Ishwar V. Basawa and David John Scott, Asymptotic optimal inference for nonergodic models, Lecture Notes in Statistics, vol. 17, Springer-Verlag, New York-Berlin, 1983. MR 688650

Rudolf Beran, Asymptotically efficient adaptive rank estimates in location models, Ann. Statist. 2 (1974), 63–74. MR 345295

P. J. Bickel, On adaptive estimation, Ann. Statist. 10 (1982), no. 3, 647–671. MR 663424

L. Birgé (1983), On estimating a density using Bellinger distance and some other strange facts, MSRI Report 045-83.

G. Bouligand (1932), Introduction à la géométrie infinitésimale directe, Gauthier-Villars, Paris.

Herman Chernoff, On the distribution of the likelihood ratio, Ann. Math. Statistics 25 (1954), 573–578. MR 65087, DOI 10.1214/aoms/1177728725

Václav Fabian and James Hannan, On estimation and adaptive estimation for locally asymptotically normal families, Z. Wahrsch. Verw. Gebiete 59 (1982), no. 4, 459–478. MR 656510, DOI 10.1007/BF00532803

R. A. Fisher (1922), On the mathematical foundations of theoretical statistics, Philos. Trans. Roy. Soc. London Ser. A. 222, 309-368.

R. A. Fisher (1925), Theory of statistical estimation, Proc. Cambridge Philos. Soc. 22, 700-725.

David A. Freedman, On the asymptotic behavior of Bayes’ estimates in the discrete case, Ann. Math. Statist. 34 (1963), 1386–1403. MR 158483, DOI 10.1214/aoms/1177703871

Ulf Grenander, Abstract inference, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1981. MR 599175

Jaroslav Hájek, Local asymptotic minimax and admissibility in estimation, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 175–194. MR 0400513

Jaroslav Hájek and Zbyněk Šidák, Theory of rank tests, Academic Press, New York-London; Academia [Publishing House of the Czechoslovak Academy of Sciences], Prague, 1967. MR 0229351

P. Hall and C. C. Heyde, Martingale limit theory and its application, Probability and Mathematical Statistics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 624435

P. Jeganathan (1980), Asymptotic theory of estimation when the limit of the loglikelihood ratios is mixed normal, Thesis, Indian Statist. Inst. Calcutta.

Yu. A. Koshevnik and B. Ya. Levit (1976), On a non-parametric analogue of the information matrix, Theory Probab. Appl. 21, 738-753.

P. Laplace (1809-1810), Approximation des formules qui sont fonctions de très grands nombres et leur application aux probabilities, Mémoires de l'Académie des Sciences, vol. 10.

Lucien Le Cam, Locally asymptotically normal families of distributions. Certain approximations to families of distributions and their use in the theory of estimation and testing hypotheses, Univ. California Publ. Statist. 3 (1960), 37–98. MR 126903

E. L. Lehmann, Nonparametrics: statistical methods based on ranks, Holden-Day Series in Probability and Statistics, Holden-Day, Inc., San Francisco, Calif.; McGraw-Hill International Book Co., New York-Düsseldorf, 1975. With the special assistance of H. J. M. d’Abrera. MR 0395032

P. W. Millar, Asymptotic minimax theorems for the sample distribution function, Z. Wahrsch. Verw. Gebiete 48 (1979), no. 3, 233–252. MR 537670, DOI 10.1007/BF00537522

P. W. Millar, Nonparametric applications of an infinite-dimensional convolution theorem, Z. Wahrsch. Verw. Gebiete 68 (1985), no. 4, 545–556. MR 772198, DOI 10.1007/BF00535344

W. Moussatat (1976), On the asymptotic theory of statistical experiments and some of its applications, Thesis, Univ. of California, Berkeley.

J. Pfanzagl, Asymptotic expansions in parametric statistical theory, Developments in statistics, Vol. 3, Academic Press, New York-London, 1980, pp. 1–97. MR 597897

Robert J. Serfling, Approximation theorems of mathematical statistics, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1980. MR 595165

S. Saks (1937), Theory of the integral, 2nd ed., Hafner, New York.

Charles Stein, Efficient nonparametric testing and estimation, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. I, University of California Press, Berkeley-Los Angeles, Calif., 1956, pp. 187–195. MR 0084921

Abraham Wald, Tests of statistical hypotheses concerning several parameters when the number of observations is large, Trans. Amer. Math. Soc. 54 (1943), 426–482. MR 12401, DOI 10.1090/S0002-9947-1943-0012401-3

M. Akahira and K. Takeuchi (1981), Asymptotic efficiency of statistical estimators: Concepts and higher order asymptotic efficiency, Lecture Notes in Statistics, vol. 7, Springer-Verlag, Berlin and New York. MR 0617375




P. Assouad (1983), Deux remarques sur l'estimation, C. R. Acad. Sci. Paris, 296, 1021-1024. MR 777600




I. Basawa and B. L. S. Prakasa Rao (1980), Statistical inference for stochastic processes, Academic Press, New York. MR 586053




I. Basawa and D. J. Scott (1983), Asymptotic optimal inference for non-ergodic models, Lecture Notes in Statistics, vol. 17, Springer-Verlag, Berlin and New York. MR 688650




R. Beran (1974), Asymptotically efficient adaptive rank estimates in location models, Ann. Statist. 2, 63-74. MR 345295




P. Bickel (1982), On adaptive estimation, Ann. Statist. 10, 647-671. MR 663424




L. Birgé (1983), On estimating a density using Bellinger distance and some other strange facts, MSRI Report 045-83.




G. Bouligand (1932), Introduction à la géométrie infinitésimale directe, Gauthier-Villars, Paris.




H. Chernoff (1954), On the distribution of the likelihood ratio, Ann. Math. Statist. 25, 573-578. MR 65087




V. Fabian and J. Hannan (1982), On estimation and adaptive estimation for locally asymptotically normal families, Z. Wahrsch. Verw. Gebiete 59, 459-478. MR 656510




R. A. Fisher (1922), On the mathematical foundations of theoretical statistics, Philos. Trans. Roy. Soc. London Ser. A. 222, 309-368.




R. A. Fisher (1925), Theory of statistical estimation, Proc. Cambridge Philos. Soc. 22, 700-725.




D. A. Freedman (1963), On the asymptotic behavior of Bayes estimates in the discrete case, Ann. Math. Statist. 34, 1386-1403. MR 158483




U. Grenander (1981), Abstract inference, Wiley, New York. MR 599175




J. Hájek (1972), Local asymptotic minimax and admissibility in estimation, Proc. Sixth Berkeley Sympos. Math. Statist, and Probab. Vol. 1, pp. 175-194. MR 400513




J. Hájek and Z. Šidák (1967), Theory of rank tests, Academia, Praha. MR 229351




P. Hall and C. C. Heyde (1980), Martingale limit theory and its application, Academic Press, New York. MR 624435




P. Jeganathan (1980), Asymptotic theory of estimation when the limit of the loglikelihood ratios is mixed normal, Thesis, Indian Statist. Inst. Calcutta.




Yu. A. Koshevnik and B. Ya. Levit (1976), On a non-parametric analogue of the information matrix, Theory Probab. Appl. 21, 738-753.




P. Laplace (1809-1810), Approximation des formules qui sont fonctions de très grands nombres et leur application aux probabilities, Mémoires de l'Académie des Sciences, vol. 10.




L. Le Cam (1960), Locally asymptotically normal families of distributions, Univ. California Publ. Statist., vol. 3, pp. 37-98. MR 126903




E. L. Lehmann (1975), Nonparametrics. Statistical methods based on ranks, Holden-Day, San Francisco, Calif. MR 395032




P. W. Millar (1979), Asymptotic minimax theorems for the sample distribution function, Z. Wahrsch. Verw. Gebiete 48, 233-252. MR 537670




P. W. Millar (1983), Nonparametric applications of an infinite dimensional convolution theorem, Preprint, Dept. Statist., Berkeley. MR 772198




W. Moussatat (1976), On the asymptotic theory of statistical experiments and some of its applications, Thesis, Univ. of California, Berkeley.




J. Pfanzagl (1980), Asymptotic expansions in parametric statistical theory, Developments in Statistics (P. R. Krishnaiah, ed.), Academic Press, New York, pp. 1-97. MR 597897




R. Serfling (1982), Approximation theorems of mathematical statistics, Wiley, New York. MR 595165




S. Saks (1937), Theory of the integral, 2nd ed., Hafner, New York.




C. Stein (1956), Efficient nonparametric testing and estimation, Proc. Third Berkeley Sympos. Math. Statist, and Probab., Vol. 1, pp. 187-195. MR 84921




A. Wald (1943), Tests of statistical hypotheses concerning several parameters when the number of observations is large, Trans. Amer. Math. Soc. 54, 426-482. MR 12401