Simultaneous credible intervals for small area estimation problems

In this paper, we fill in an important research gap in small area literature, namely the problem of constructing simultaneous credible intervals. We illustrate how the Bayesian approach can be applied to develop different simultaneous credible interval procedures. The utility of our method is illustrated through simulation and data analysis.

[1]  K. Wolter Introduction to Variance Estimation , 1985 .

[2]  J. Rao Small Area Estimation , 2003 .

[3]  Noel A Cressie,et al.  REML estimation in empirical Bayes smoothing of census undercount , 1992 .

[4]  Malay Ghosh,et al.  Bayesian Methods for Finite Population Sampling , 1997 .

[5]  Jiming Jiang,et al.  Empirical best prediction for small-area inference based on generalized linear mixed models , 2003 .

[6]  J. Berger Statistical Decision Theory and Bayesian Analysis , 1988 .

[7]  J. Rao,et al.  On measuring the variability of small area estimators under a basic area level model , 2005 .

[8]  W. Johnson,et al.  A Bayesian perspective on the Bonferroni adjustment , 1997 .

[9]  A. Tamhane,et al.  Multiple Comparison Procedures , 1989 .

[10]  D. Berry,et al.  Bayesian perspectives on multiple comparisons , 1999 .

[11]  Rupert G. Miller Simultaneous Statistical Inference , 1966 .

[12]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[13]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[14]  Jiming Jiang,et al.  Estimation of Finite Population Domain Means , 2006 .

[15]  Grace M. Carter,et al.  Empirical Bayes Methods Applied to Estimating Fire Alarm Probabilities , 1974 .

[16]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[17]  V. Barnett,et al.  Applied Linear Statistical Models , 1975 .

[18]  D. Pfeffermann Small Area Estimation‐New Developments and Directions , 2002 .

[19]  Jiming Jiang,et al.  Mixed model prediction and small area estimation , 2006 .

[20]  James G. Scott,et al.  An exploration of aspects of Bayesian multiple testing , 2006 .

[21]  P. Lahiri,et al.  A new class of average moment matching priors , 2008 .

[22]  Nicholas T. Longford,et al.  Missing Data and Small-Area Estimation , 2005 .

[23]  B. Efron,et al.  Data Analysis Using Stein's Estimator and its Generalizations , 1975 .

[24]  C. Morris Parametric Empirical Bayes Confidence Intervals , 1983 .

[25]  R. Fay,et al.  Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data , 1979 .