Extension of a two-stage conditionally unbiased estimator of the selected population to the bivariate normal case

Communications in Statistics - Theory and Methods

Volumn 36, Issue 4, 2007, Pages 801-813

  Sill, Michael W ^a,c   Sampson, Allan R ^b  

^a UNIVERSITY AT BUFFALO   (United States)

^b UNIVERSITY OF PITTSBURGH   (United States)

^c ROSWELL PARK CANCER INSTITUTE   (United States)

Author keywords

Biased; Bivariate normal distribution; Clinical trial; Conditional estimation; Correlated observations; Estimation after selection; Maximum; Ranking and selection; Surrogate; UMVUE

Indexed keywords

COVARIANCE MATRIX; ESTIMATION; PROBABILITY DISTRIBUTIONS;

BIVARIATE NORMAL DISTRIBUTION; CLINICAL TRIAL; CONDITIONAL ESTIMATION; CORRELATED OBSERVATIONS; ESTIMATION AFTER SELECTION; UNIFORMLY MINIMUM VARIANCE CONDITIONALLY UNBIASED ESTIMATOR (UMVCUE);

POPULATION STATISTICS;

EID: 33947600693     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920601034072     Document Type: Article

References (28)

1. Bookman, M. A. et al. (2006). GOG 182-ICON5: 5 arm phase III randomized trial of paclitaxel (P) and carboplatin (C) vs combinations with gemcitabine (G), PEG-liposomol doxorubicin (D), or topotecan (T) in patients (pts) with advanced-stage epithelial ovarian (EOC) or primary peritoneal (PPC) carcinoma. Proceedings to the Annual Meeting of the American Society of Clinical Oncology, Supplement to to Journal of Clinical Oncology. 24(188 Part I of II): p256s # 5002.
2. Cohen, A., Sackrowitz, H. B. (1982). Estimating the mean of the selected population In: Gupta, S. S., Berger, J. O., eds. Statistical Decision Theory Related Topics-III. Vol. 1. New York: Academic Press, pp. 243-270.
3. Cohen, A., Sackrowitz, H. B. (1988). A decision theory formulation for population selection followed by estimating the mean of the selected population. In: Gupta, S. S., Berger, J. O., eds. Statistical Decision Theory Related Topics-IV. Vol. 2. New York: Springer-Verlag, pp. 33-36.
4. Cohen, A., Sackrowitz, H. B. (1989). Two stage conditionally unbiased estimators of the selected mean. Statist. Probab. Lett. 8(3):273-278.
5. Dahiya, R. C. (1974). Estimation of the mean of the selected population. J. Amer. Statist. Assoc. 69:226-230.
6. Deshpande, J. V., Fareed, T. P. M. (1995). A note on conditionally unbiased estimation after selection. Statist. Probab. Lett. 22:17-23.
7. Fareed, T. P. M. (1995). Two stage conditionally unbiased estimation following selection. J. Ind. Statist. Assoc. 33(2):123-135.
8. Fong, D. K. H. (1989). A Bayesian approach to the comparison of two means. Commun Statist. Theor. Meth. 18(10):3785-3800.
9. Gupta, S. S., Miescke, K. J. (1990). On finding the largest normal mean and estimating the selected mean. Sankhya Ser. B 52:144-157.
10. Hsieh, H. (1980). On estimating the mean of the selected population with unknown variance. Commun. Statist. Theor. Meth. A10:1869-1878.
11. Misra, N., Singh, G. N. (1993). On the UMVUE for estimating the parameter of the selected exponential population. J. Ind. Statist. Assoc. 31:61-69.
12. Misra, N., van der Meulen, E. C. (2001). On estimation following selection from nonregular distributions. Commun. Statist. Theor. Meth. 30(12):2543-2561.
13. Misra, N., van der Meulen, E. C. (2003). On estimating the mean of the selected normal population under the LINEX loss function. Metrika 58(2):173-183.
14. Parsian, A., Farsipour, N. S. (2000). Estimation of the mean of the selected population under the asymmetric loss function. Metrika 50(2):89-107.
15. Preez, J. P., Venter, J. H. (1987). An estimator for the means of normal populations. Comm. Statist. Theor. Meth. 16(2): 593-612.
16. Robbins, H. (1988). The U-V method of estimation. In: Gupta, S. S., Berger, J. O., eds. Statistical Decision Theory Related Topics-IV. Vol. 1. New York: Springer-Verlag, pp. 265-270.
17. Sackrowitz, H. B., Samuel-Cahn, E. (1984). Estimation of the mean of the selected negative exponential population. J. Roy. Statist. Soc. Ser. B 46:242-249.
18. Sampson, A. R., Sill, M. W. (2005). Drop-the-losers design: normal case. Biometrical J. 47:257-268.
19. Sarkadi K. (1967), Estimation after selection. Studia Scientiarum Mathematicarum Hungarica 2:341-350.
20. Song, R. (1992). On estimating the mean of the selected uniform population. Commun. Statist. Theor. Meth. 21(9):2707-2719.
21. Stein, C. (1964). Contribution to the discussion of Bayesian and non-Bayesian decision theory. Handout, Institute of Mathematical Statistics Meeting, Amherst, MA.
22. Tappin, L. (1992). Unbiased estimation of the parameter of a selected binomial population. Commun. Statist. Theor. Meth. 21(4):1067-1083.
23. Vellaisamy, P. (1992). Average worth and simultaneous estimation of the selected subset. Ann. Inst. Statist. Math. 44:551-562.
24. Vellaisamy, P. (1993). On UMVU estimation following selection. Commun. Statist. Theor. Meth. 22:1031-1043.
25. Vellaisamy, P. (1997). Simultaneous estimation of the selected subset of uniform populations. J. Appl. Stat. Sci. 5(1):39-46.
26. Vellaisamy, P., Sharma, D. (1988). Estimation of the mean of the selected gamma population. Commun. Statist. Theor. Meth. 17(8):2797-2817.
27. Vellaisamy, P., Kumar, S., Sharma, D. (1988). Estimating the mean of the selected uniform population. Commun Statist. Theor. Meth. 17(10):3447-3475.
28. Venter, J. H. (1988). Estimation of the mean of the selected population. Commun. Statist. Theor. Meth. 17(3):791-805.