Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

An Integrated Sequential Inference Approach for the Normal Mean

  • Almahmeed, M.A. (Department of Quantitative Methods and Information Systems, Kuwait University) ;
  • Hamdy, H.I. (Department of Quantitative Methods and Information System Kuwait University, Department of Mathematics and Statistics, University of Vermont, Burlington) ;
  • Alzalzalah, Y.H. (Department of Quantitative Methods and Information Systems, Kuwait University) ;
  • Son, M.S. (Department of Mathematics and Statistics, University of Vermont, Burlington)
  • Published : 2002.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

A unified framework for statistical inference for the mean of the normal distribution to derive point estimates, confidence intervals and statistical tests is proposed. This optimal design is justified after investigating the basic information and requirements that are possible and impossible to control when specifying practical and statistical requirements. Point estimation is only credible when viewed in the larger context of interval estimation, since the information required for optimal point estimation is unspecifiable. Triple sampling is proposed and justified as a reasonable sampling vehicle to achieve the specifiable requirements within the unified framework.

Keywords

References

  1. Metrika v.37 Sequential estimation of linear models in three stages Almahmeed, M. A.;Hamdy, H. I.
  2. Journal of the Royal Statistical Society v.B15 Sequential estimation Anscombe, F. J.
  3. The Annals of Statistics v.10 Bounded regret of a sequential procedure for estimation of the mean Chow, Y. S.;Martinsek, A. T.
  4. The Annals of Mathematical Statistics v.36 On the asymptotic theory of fixed width sequential confidence intervals for the mean Chow, Y. S.;Robbins, H.
  5. The Annals of Statistics v.9 The performance of a sequential procedure for the estimation of the mean Chow, Y. S.;Yu, K. F.
  6. Metron v.31 Type Ⅱ error performance of triple sampling fixed precision confidence intervals for the normal mean Costanza, M. C.;Hamdy, H. I.;Haugh, L. D.;Son, M. S.
  7. Biometrika v.39 Estimation by double sampling Cox, D. R.
  8. Communications in Statistics v.A8 Sequential point estimation of the mean when the distribution is unspecified Ghosh, M.;Mukhopadhyay, N.
  9. The Annals of Statistics v.8 Sequential point estimation of the difference of two normal means Ghosh, M.;Mukhopadhyay, N.
  10. The Annals of Statistics v.9 Asymptotic theory of triple sampling for sequential estimation of a mean Hall, P.
  11. Journal of the Royal Statistical Society v.B45 Sequential estimation saving sampling operations Hall, P.
  12. Scandinavian Journal of Statistics v.15 Remarks on the asymptotic theory of triple sampling estimation of the normal mean Hamdy, H. I.
  13. South African Statistical Journal v.31 Performance of fixed width confidence intervals under type Ⅱ errors: The exponential case Hamdy, H. I.
  14. Statistics v.28 A certain accelerated sequential procedure to construct simultaneous confidence region : The exponential case Hamdy, H. I.;Al-Mahmeed, M.;Al-Zalzalah, Y.
  15. Annals of the Institute of Statistical Mathematics v.40 Triple stage point estimation for the exponential location parameter Hamdy, H. I.;Mukhopadhyay, N.;Costanza, M. C.;Son, M. S.
  16. The American Statistician v.43 How appropriate are popular sample size formulas Kupper, L. L.;Hafner, K. B.
  17. Journal of the American Statistical Association v.83 Negative regret, optional stopping and the elimination of outliers Martinsek, A. T.
  18. Sequential Analysis v.4 A note on three-stage and sequential point estimation procedures for a normal mean Mukhopadhyay, N.
  19. Sequential Analysis v.6 Three-stage point estimation procedures for a normal mean Mukhopadhyay, N.;Hamdy, H. I.;Al-Mahmeed, M.;Costanza, M. C.
  20. Probability & Statistics-The Harald Cramer Volume Sequential estimation of the mean of a normal population Robbins, H.
  21. Annals of the Institute of Statistical Mathematics v.49 Controlling type Ⅱ error while constructing triple sampling fixed precision confidence intervals for the normal mean Son, M. S.;Haugh, L. D.;Hamdy, H. I.;Costanza, M. C.
  22. The Annals of Mathematical Statistics v.37 On the asymptotic efficiency of a sequential procedure for estimating the mean Starr, N.
  23. Proceedings of the National Academy of Sciences of the United States of America v.63 Remarks on a sequential point estimation Starr, N.;Woodroofe, M. B.
  24. The Annals of Mathematical Statistics v.17 A two stage test for a linear hypothesis whose power is independent of the variance Stein, C.
  25. The Annals of Statistics v.5 Second order approximation for sequential point and interval estimation Woodroofe, M.
  26. The Annals of Statistics v.7 Asymptotic local minimaxity in sequential point estimation Woodroofe, M.
  27. New Perspectives in Theoretical and Applied Statistics Asymptotically optimal sequential point estimation in three stages Woodroofe, M.;M. L. Puri(ed.);J. P. Vilaplana(ed.);W. Wertz(ed.)