Browse > Article

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)
Publication Information
Journal of the Korean Statistical Society / v.31, no.4, 2002 , pp. 415-431 More about this Journal
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
Confidence intervals; cost functions; decision theory; fixed precision; hypothesis tests; Fisher information; loss functions; opportunity cost; point estimation; regret; risk functions; sampling cost; sequential sampling; squared error loss; triple sampling; type II error;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Asymptotic theory of triple sampling for sequential estimation of a mean /
[ Hall, P. ] / The Annals of Statistics   ScienceOn
2 Remarks on the asymptotic theory of triple sampling estimation of the normal mean /
[ Hamdy, H. I. ] / Scandinavian Journal of Statistics
3 Asymptotically optimal sequential point estimation in three stages /
[ Woodroofe, M.;M. L. Puri(ed.);J. P. Vilaplana(ed.);W. Wertz(ed.) ] / New Perspectives in Theoretical and Applied Statistics
4 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. ] / Annals of the Institute of Statistical Mathematics   ScienceOn
5 A note on three-stage and sequential point estimation procedures for a normal mean /
[ Mukhopadhyay, N. ] / Sequential Analysis
6 Three-stage point estimation procedures for a normal mean /
[ Mukhopadhyay, N.;Hamdy, H. I.;Al-Mahmeed, M.;Costanza, M. C. ] / Sequential Analysis
7 A two stage test for a linear hypothesis whose power is independent of the variance /
[ Stein, C. ] / The Annals of Mathematical Statistics
8 Second order approximation for sequential point and interval estimation /
[ Woodroofe, M. ] / The Annals of Statistics   ScienceOn
9 The performance of a sequential procedure for the estimation of the mean /
[ Chow, Y. S.;Yu, K. F. ] / The Annals of Statistics   ScienceOn
10 How appropriate are popular sample size formulas /
[ Kupper, L. L.;Hafner, K. B. ] / The American Statistician   ScienceOn
11 Sequential point estimation of the difference of two normal means /
[ Ghosh, M.;Mukhopadhyay, N. ] / The Annals of Statistics   ScienceOn
12 Remarks on a sequential point estimation /
[ Starr, N.;Woodroofe, M. B. ] / Proceedings of the National Academy of Sciences of the United States of America   ScienceOn
13 Sequential estimation /
[ Anscombe, F. J. ] / Journal of the Royal Statistical Society
14 Triple stage point estimation for the exponential location parameter /
[ Hamdy, H. I.;Mukhopadhyay, N.;Costanza, M. C.;Son, M. S. ] / Annals of the Institute of Statistical Mathematics
15 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. ] / Metron
16 A certain accelerated sequential procedure to construct simultaneous confidence region : The exponential case /
[ Hamdy, H. I.;Al-Mahmeed, M.;Al-Zalzalah, Y. ] / Statistics   ScienceOn
17 Sequential point estimation of the mean when the distribution is unspecified /
[ Ghosh, M.;Mukhopadhyay, N. ] / Communications in Statistics
18 Sequential estimation saving sampling operations /
[ Hall, P. ] / Journal of the Royal Statistical Society
19 Negative regret, optional stopping and the elimination of outliers /
[ Martinsek, A. T. ] / Journal of the American Statistical Association   ScienceOn
20 Bounded regret of a sequential procedure for estimation of the mean /
[ Chow, Y. S.;Martinsek, A. T. ] / The Annals of Statistics   ScienceOn
21 On the asymptotic theory of fixed width sequential confidence intervals for the mean /
[ Chow, Y. S.;Robbins, H. ] / The Annals of Mathematical Statistics   ScienceOn
22 Sequential estimation of linear models in three stages /
[ Almahmeed, M. A.;Hamdy, H. I. ] / Metrika
23 On the asymptotic efficiency of a sequential procedure for estimating the mean /
[ Starr, N. ] / The Annals of Mathematical Statistics   ScienceOn
24 Performance of fixed width confidence intervals under type Ⅱ errors: The exponential case /
[ Hamdy, H. I. ] / South African Statistical Journal
25 Sequential estimation of the mean of a normal population /
[ Robbins, H. ] / Probability & Statistics-The Harald Cramer Volume
26 Asymptotic local minimaxity in sequential point estimation /
[ Woodroofe, M. ] / The Annals of Statistics
27 Estimation by double sampling /
[ Cox, D. R. ] / Biometrika