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Empirical Bayes Confidence Intervals for Means of Natural Exponential Family‐Quadratic Variance Function Distributions with Application to Small Area Estimation
Author(s) -
GHOSH MALAY,
MAITI TAPABRATA
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00597.x
Subject(s) - mathematics , statistics , exponential family , bayes' theorem , natural exponential family , coverage probability , confidence interval , population , context (archaeology) , credible interval , sample size determination , exponential function , bayesian probability , geography , demography , archaeology , sociology , mathematical analysis
. The paper develops empirical Bayes (EB) confidence intervals for population means with distributions belonging to the natural exponential family‐quadratic variance function (NEF‐QVF) family when the sample size for a particular population is moderate or large. The basis for such development is to find an interval centred around the posterior mean which meets the target coverage probability asymptotically, and then show that the difference between the coverage probabilities of the Bayes and EB intervals is negligible up to a certain order. The approach taken is Edgeworth expansion so that the sample sizes from the different populations need not be significantly large. The proposed intervals meet the target coverage probabilities asymptotically, and are easy to construct. We illustrate use of these intervals in the context of small area estimation both through real and simulated data. The proposed intervals are different from the bootstrap intervals. The latter can be applied quite generally, but the order of accuracy of these intervals in meeting the desired coverage probability is unknown.