Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Sequential Estimation with $\beta$-Protection of the Difference of Two Normal Means When an Imprecision Function Is Variable

  • Kim, Sung-Lai (Department of Mathematics, Chungnam National University) ;
  • Kim, Sung-Kyun (Department of Mathematics, Chungnam National University)
  • Published : 2002.09.01
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Abstract

For two normal distribution with unknown means and unknown variances, a sequential procedure for estimating the difference of two normal means which satisfies both the coverage probability condition and the $\beta$-protection is proposed under some smoothness of variable imprecision function, and the asymptotic normality of the proposed stopping time after some centering and scaling is given.

Keywords

References

  1. Proceedings of Cambridge Philosophical Society v.48 Large sample theory of sequential estimation Anscombe, F.J. https://doi.org/10.1017/S0305004100076386
  2. The Annals of mathematical Statistics v.36 On the asymptotic theory of fixed width comfidence intervals for the means Chow, Y.S.;Robbins, H.
  3. Sequential Analysis v.9 An adaptive biased coin design for the Behrens-Fisher problem Eisele, J.R. https://doi.org/10.1080/07474949008836217
  4. Sequential Analysis v.8 Sequential confidence sets with bata-protection in multiparameter families Fahker-Zakeri
  5. The Annals of Statistics v.8 Sequential point estimation of the difference of two normal mean Ghosh, M.;Mukhopadhyay, N. https://doi.org/10.1214/aos/1176344906
  6. Ph.D. Dissertation Sequential and Non-sequential Intervals with Guaranteed Coverage Probability and Beta Protection Juhlin, K.D.
  7. Journal of the Korean Statistical Society v.19 Sequential confidence intervals for the mean with β-protection in a certain parameter space Kim, S.L.
  8. Journal of the Korean Statistical Society v.26 Sequential confidence intervals for the mean with β-protection for a linear function of two normal means Kim, S.L.
  9. The Annals Mathematical Statistics v.38 Sequential analogue of the Bhrens-Fisher Problem Robbins, H.;Simons, G.;Starr, N. https://doi.org/10.1214/aoms/1177698694
  10. Communications in Statistics-Theory and Method A v.10 Confidence sets based on sequential test Wijsman, R.A. https://doi.org/10.1080/03610928108828179
  11. Statistical Decision Theory and Related Topics Ⅲ v.2 Sequential confidence sets: Estimation-oriented versus Test-oriented construction Wijsman, R.A.
  12. Sequential Analysis v.2 Sequenctial estimation and test-oriented confildence intervals for μ/σ in a normal population Wijsman, R.A. https://doi.org/10.1080/07474948308836033
  13. Adaptive Statistical Procedures and Related Topics Sequential confidence intervals with beta-protection in one-parameter families Wijsman, R.A.
  14. The Annals of Mathematical Statistics v.21 Minimax estimates of the mean of a normal distribution with unknown variance Wolfowitz, J. https://doi.org/10.1214/aoms/1177729840