Publication Cover
Sequential Analysis
Design Methods and Applications
Volume 6, 1987 - Issue 3
41
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

On the attainment of the cramer-rao bound in the sequential case

Pages 267-288 | Published online: 29 Mar 2007

References

  • Barndorff-Nielsen , O. 1978 . Information and Exponential Families in Statistical Theory , New York : Wiley .
  • Chow , Y. S. , Robbins , H. and Teicher , H. 1965 . Moments of randomly stopped sums . Ann. Math. Statiste , 36 : 789 – 799 .
  • Degroot , M. H. 1959 . Unbiased sequential estimation for binomial populations . Ann. Math. Statist , 30 : 80 – 101 .
  • Dvoretzky , A. , Kiefer , J. and Wolfowitz , J. 1953 . Sequential decision problems for processes with continuous time parameter Problems of estimation . Ann.Math.Statist , 24 : 403 – 415 .
  • Girshlck , M. A. and Savage , L. J. Bayes and minimax estimates for quadratic loss functions . proc.Second Berkeley Symp.on Math.Statist.and Prob . pp. 53 – 73 .
  • Haldane , J. B. S. 1945 . On a method of estimating frequencies . Biometrika , 33 : 222 – 225 .
  • Hodges , J. L. and Lehmann , E. L. Some applications of the Cramér Rao inequality . Proc.Second Berkeley Symp.on Math. Statist and Prob . pp. 13 – 22 .
  • Ibragimov , I. A. and Khasminskii , R. Z. 1974 . sequential estimation . Theory of Prob. and Its Appl. , 19 : 233 – 244 .
  • Kiefer , J. 1957 . Invariance, minimax sequential estimation, and continuous time processes . Ann. Math. Statist , 28 : 573 – 601 .
  • Lehmann , E. L. and Stein , C. 1950 . Completeness in the sequential case . Ann. Math. Statist , 21 : 376 – 385 .
  • Linnik , Yu. V. and Romanovsky , I. V. Some new results in sequential estimation theory . Proc.Sixth Berkeley Symp. on Math. Statist. and Prob . pp. 85 – 96 .
  • Morris , C. N. 1982 . Natural exponential families with quadratic variance functions . Ann. Statist. , 10 : 65 – 80 .
  • Seth , G. R. 1949 . On the variance of estimates . Ann. Math. Statist. , 20 : 1 – 27 .
  • Simons , G. 1980 . Sequential estimators and the Cramér-Rao lower bound . J. Stat. Plan. and Inf. , 4 : 67 – 74 .
  • Stefanov , V. 1985 . On efficient stopping times . Stoch. proc. and Appl. , 19 : 305 – 314 .
  • Trybula , S. 1968 . Sequential estimation in processes with independent increments . Dissertationes Mathematicae , 60 : 1 – 50 .
  • Wald , A. Asymptotic minimax solutions of sequential point estimation problems . Proc.Second Berkeley Symp. on Math. Statist. and Prob . pp. 1 – 11 .
  • Wasan , M. T. 1964 . Sequential optimum procedures for unbiased estimation of a binomial parameter . Technometrics , 6 : 259 – 271 .
  • Whittle , P. and Lane , R. O. D. 1967 . A class of situations in which a sequential estimation procedure is non sequential . Biometrika , 54 : 229 – 234 .
  • Wijsman , R. A. 1973 . On the attainment of the Cramér-Rao lower bound . Ann. Statist. , 1 : 538 – 542 .
  • Wijsman , R. A. 1979 . “ Stopping time of invariant sequential probability ratio tests ” . In Developments in Statistics , 235 – 314 . Academic Press .
  • Wolfowitz , J. 1946 . On sequential binomial estimation . Ann. Math. Statist. , 17 : 489 – 493 .
  • Wolfowitz , J. 1947 . The efficiency of sequential estimates and Walds equation for sequential processes . Ann. Math. Statist. , 18 : 215 – 230 .
  • Wolfowitz , J. 1950 . Minimax estimates of the mean of a normal distribution with known variance . Ann. Math. Statist. , 21 : 218 – 230 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.