Biometrika Advance Access published online on April 23, 2008
Biometrika, doi:10.1093/biomet/asn008
Articles |
A new class of average moment matching priors
Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A. ganesh{at}math.umd.edu
Joint Program in Survey Methodology, University of Maryland, College Park, Maryland 20742, U.S.A. plahiri{at}survey.umd.edu
Received for publication 1 August 2006. Revision received 1 November 2007.
We derive a new class of priors for the variance component in the Fay–Herriot model, a mixed regression model widely used in small area estimation. This class includes the well-known uniform or superharmonic prior. Through simulation we illustrate the use of our class of priors.
Key Words: Hierarchical Bayes Matched priors Mixed linear model
References
-
Berger J. Statistical Decision Theory and Bayesian Analysis (1985) 2nd ed. New York: Springer.
Bernardo J. M. Reference analysis. In: Handbook of Statistics—Dey D. K., Rao C. R., eds. (2005) 25. Amsterdam: Elsevier. 17–90.[CrossRef]
Datta G. S., Lahiri P. A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statist. Sinica (2000) 10:613–27.
Datta G. S., Mukherjee R. Probability Matching Priors: Higher Order Asymptotics. (2004) New York: Springer.
Datta G. S., Rao J. N. K., Smith D. D. On measuring the variability of small area estimators under a basic area level model. Biometrika (2005) 92:183–96.
Fay R. E., Herriot R. A. Estimates of income for small places: an application of James-Stein procedures to census data. J. Am. Statist. Assoc. (1979) 74:269–77.[CrossRef][ISI]
Jiang J. REML estimation: asymptotic behavior and related topics. Ann. Statist. (1996) 24:255–86.[CrossRef]
Morris C. N., Christiansen C. L. Hierarchical models for ranking and for identifying extremes with applications. In: Bayesian Statistics—Bernardo J. M., Berger J. O., Dawid A. P., Smith A. F. M., eds. (1996) 5. Oxford: Oxford University Press. 277–96.
Morris C. N. Parametric empirical Bayes inference: theory and applications. J. Am. Statist. Assoc. (1983) 78:47–59.[CrossRef][ISI]
Morris C. N. Parametric empirical Bayes confidence intervals. In: Proc. Conf. Sci. Infer. Data Anal. Robustness—Box G. E. P., Leonard T., Wu C. F. J., eds. (1983) New York: Academic Press. 25–50.
Rao J. N. K. Small Area Estimation. (2003) New York: Wiley.
Robert C. P., Casella G. Monte Carlo Statistical Methods. (1999) New York: Springer.
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