Estimating A Ratio Of The Variances In A Balanced One-Way Random Effects Model

Statistics and Risk Modeling

Volumn 16, Issue 2, 1998, Pages 163-180

  Ye, Keying ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Admissibility; Bayes estimator; Jeffreys prior; risk functions; the reference prior

Indexed keywords

EID: 67649351640     PISSN: 21931402     EISSN: 21967040     Source Type: Journal    
DOI: 10.1524/strm.1998.16.2.163     Document Type: Article

References (18)

1. Berger, J. (1985). Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York.
2. Berger, J. and Bernardo, J. (1992a). On the development of the reference prior method. In Bayesian Statistic 4, (Bernardo, J.M., Berger, J.O., Dawid, A.P. and Smith, A.F.M. eds), Oxford University Press: London, 35-60.
3. Berger, J. and Bernardo, J. (1992b). Reference priors in a variance components problem. Proceedings of the Indo-USA Workshop on Bayesian Analysis in Statistics and Econometrics, (P. Goel, ed.) New York: Springer, 323-340.
4. Bernardo, J. (1979). Reference posterior distributions for Bayesian inference (with discussion). J.R.Statist.Soc., B41,113-147.
5. Blyth, C. R. (1951). On minimax statistical decision procedures and their admissibility. Ann. Math. Statist. 22,22-42.
6. Box, G. and Tiao, G. (1973). Bayesian Inference in Statistical Analysis. Addison-Wesly, Readings, Massachusetts.
7. Chaloner, K. (1987). ABayesian approach to the estimation of variance component for the unbalanced one-way random model. Technometrics, 29, 323-337.
8. Datta, G. and Ghosh, M. (1995a). Hierarchical Bayes estimators of the error variance in one-way ANOVA models. J. Statist. Plan. Inf. 45, 399-411.
9. Datta, G. and Ghosh, M. (1996). On the invariance of noninformative priors. Ann. Statistics, 64,141-159.
10. Graybill, F.A. (1976). Theory and Application of the Linear Model. Duxbury Press, North Scituate, Massachusettes.
11. Graybill, F.A., Martin, F. and Godfrey, G. (1956). Confidence intervals for variance ratios specifying genetic heritability. Biometrics, 12,99-109.
12. Klotz, J.H., Milton, R.C., and Zacks, S. (1969). Mean square efficiency of estimators of variance components. Journal of American Statistical Association, 64,1383-1402.
13. Palmer, J. L. and Broemeling, L. D. (1990). A comparison of Bayes and maximum likelihood estimation of the intraclass correlation coefficient. Commun. Statist. -Theory Meth., 19,953-975.
14. Portnoy, S. (1971). Formal Bayes estimation with application to a random effect model. Ann. Math. Statist., 42,1379-1402.
15. Stein, C. (1955). A necessary and sufficient condition for admissibility. Ann. Math. Statist., 26, 518-522.
16. Tiao, G.C. and Tan, W.Y. (1965). Bayesian analysis of random-effect models in the analysis of variance. I. Posterior distribution of variance-components. Biometrika, 52,37-53.
17. Wang, C.S., Rutledge, J.J., and Gianola, D. (1993). Marginal inferences about variance components in a mixed linear model using Gibbs sampling. Genet. Sel. Evol, 25,41-62.
18. Ye, K. (1994). Bayesian reference prior analysis on the ratio of variances for the balanced one-way random effect model. J. of Statistical Planning and Inference, 41, 267-280.