2003, Volume 65, Pt. 3, 612--625

Modelling  Small Area Effects Using Mixture Of Gaussians


TAPABRATA MAITI, Iowa State University, Ames, Iowa, USA

SUMMARY. The importance of mixed effects model is well known for the small area estimation problem. Gaussian distributions are commonly used for the small area specific random effects. The mixing distribution is used to `borrow strength' from the other small areas and the Gaussian mixing distribution is mathematically convenient for inference purposes. However, this choice places a strong assumption about the shape of the mixing distribution that may not be valid. In this article, we focus on misspecification in unit specific small area model with random intercept commonly known as type II model. We propose a Gaussian mixture with an unknown number of components to model the prior distribution of the random intercept in a hierarchical Bayesian framework.

AMS (1991) subject classification. 62C12, 62P25.

Key words and phrases. Bayes estimator, Gibbs sampling, hierarchical Bayes, Markov Chain Monte Carlo, Metropolis-Hastings algorithm, prior distribution, reversible jump MCMC.

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