Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
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.

References [Enhancements On Off] (What's this?)

  • 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, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. Probability and Mathematical Statistics. 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
  • R. Beran (1974), Asymptotically efficient adaptive rank estimates in location models, Ann. Statist. 2, 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.
  • H. Chernoff (1954), On the distribution of the likelihood ratio, Ann. Math. Statist. 25, 573-578. MR 65087
  • 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, https://doi.org/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.
  • D. A. Freedman (1963), On the asymptotic behavior of Bayes estimates in the discrete case, Ann. Math. Statist. 34, 1386-1403. MR 158483
  • Ulf Grenander, Abstract inference, John Wiley & Sons, Inc., New York, 1981. Wiley Series in Probability and Mathematical Statistics. 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, Martingale limit theory and its application, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. Probability and Mathematical Statistics. 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, Asymptotic minimax theorems for the sample distribution function, Z. Wahrsch. Verw. Gebiete 48 (1979), no. 3, 233–252. MR 537670, https://doi.org/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, https://doi.org/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, John Wiley & Sons, Inc., New York, 1980. Wiley Series in Probability and Mathematical Statistics. 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

Review Information:

Reviewer: Lucien Le Cam
Journal: Bull. Amer. Math. Soc. 11 (1984), 392-400
DOI: https://doi.org/10.1090/S0273-0979-1984-15326-6
American Mathematical Society