Empirical Bayes confidence intervals shrinking both means and variances

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 71, Issue 1, 2009, Pages 265-285

  Gene Hwang, J T ^a,b   Qiu, Jing ^c   Zhao, Zhigen ^a  

^a Department of Obstetrics Gynecology   (United States)

^b NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^c UNIVERSITY OF MISSOURI   (United States)

Author keywords

Multiple testing; Shrinking both means and variances; Shrinking means; Shrinking variances; Simultaneous confidence intervals

Indexed keywords

EID: 58149359201     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2008.00681.x     Document Type: Article

References (28)

1. Berger, J. O. (1985) Statistical Decision Theory and Bayesian Analysis, 2nd edn. New York : Springer.
2. Casella, G. Hwang, J. T. G. (1983) Empirical Bayes confidence sets for the mean of a multivariate normal distribution. J. Am. Statist. Ass., 78, 688 698.
3. Casella, G. Hwang, J. T. G. (1991) Evaluating confidence sets using loss functions. Statist. Sin., 1, 159 173.
4. Casella, G., Hwang, J. T. G. Robert, C. (1993) A Paradox in decision-theoretic interval estimation. Statist. Sin., 3, 141 155.
5. Choe, S. E., Boutros, M., Michelson, A. M., Church, G. M. Halfon, M. S. (2005) Preferred analysis methods for Affymetrix GeneChips revealed by a wholly defined control dataset. Genome Biol., 6 R16.
6. Cui, X., Hwang, J. T. G., Qiu, J., Blades, N. J. Churchill, G. A. (2005) Improved statistical tests for differential gene expression by shrinking variance components estimates. Biostatistics, 6, 59 75.
7. Efron, B. (2006) Minimum volume confidence regions for a multivariate normal mean vector. J. R. Statist. Soc. B, 68, 655 670.
8. Efron, B. Tibshirani, R. (1993) An Introduction to the Bootstrap. London : Chapman and Hall.
9. He, K. (1992) Parametric empirical Bayes confidence intervals based on James-Stein estimator. Statist. Decisn, 10, 121 132.
10. Hwang, J. T. G. Liu, P. (2007) Optimal tests shrinking both means and variances applicable to microarray data analysis. To be published.
11. Joshi, V. (1969) Admissibility of the usual confidence sets for the mean of a univariate or bivariate normal population. Ann. Math. Statist., 40, 1042 1067.
12. Kendziorski, C., Newton, M., Lan, H. Gould, M. (2003) On parametric empirical Bayes methods for comparing multiple groups using replicated gene expression profiles. Statist. Med., 22, 3899 3914.
13. Laird, N. M. Louis, T. A. (1987) Empirical Bayes confidence intervals based on bootstrap samples (with discussion). J. Am. Statist. Ass., 82, 739 757.
14. Lo, K. Gottardo, R. (2007) Flexible empirical Bayes models for differential gene expression. Bioinformatics, 23, 328 335.
15. Lönnstedt, I. Speed, T. P. (2002) Replicated microarray data. Statist. Sin., 12, 31 46.
16. Milton, J. S. Arnold, J. C. (2002) Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, 4th edn. New York : McGraw-Hill.
17. Morris, C. (1983a) Parametric empirical Bayes confidence intervals. In Scientific Inference, Data Analysis and Robustness, 25 50. New York : Academic Press.
18. Morris, C. (1983b) Parametric empirical Bayes inference: theory and applications. J. Am. Statist. Ass., 78, 47 55.
19. Qiu, J. (2004) Sharp simultaneous intervals for the means of selected populations with application to microarray data analysis. PhD Thesis. Cornell University, Ithaca.
20. Qiu, J. Hwang, J. T. G. (2007) Sharp simultaneous intervals for the means of selected populations with application to microarray data analysis. Biometrics, 63, 767 776.
21. Qiu, J. Hwang, J. T. G. (2008) Reply to Dr. Ekkehard Glimm's letter. Biometrics, to be published.
22. Samworth, R. (2005) Small confidence sets for the mean of a spherically symmetric distribution. J. R. Statist. Soc. B, 67, 343 361.
23. Smyth, G. K. (2004) Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statist. Appl. Genet. Molec. Biol., 3, article 3.
24. Stein, C. M. (1962) Confidence sets for the mean of a multivariate normal distribution (with discussion). J. R. Statist. Soc. B, 24, 265 296.
25. Tong, T. Wang, Y. (2007) Optimal shrinkage estimation of variances with applications to microarray data analysis. J. Am. Statist. Ass., 102, 113 122.
26. Tseng, Y. L. Brown, L. D. (1997) Good exact confidence sets for a multivariate normal mean. Ann. Statist., 25, 2228 2258.
27. Tusher, V. G., Tibshirani, R. Chu, G. (2001) Significance analysis of microarrays applied to the ionizing radiation response. Proc. Natn. Acad. Sci. USA, 98, 5116 5121.
28. Wright, G. W. Simon, R. M. (2003) A random variance model for detection of differential gene expression in small microarray experiments. Bioinformatics, 19, 2448 2455.