A NOTE ON SMALL AREA ESTIMATIONS FOR RARE EVENT DATA

Key-Il Shin (Korea), Sang Eun Lee (Korea) and Yonghee Kim-Park (U. S. A.)

Received May 18, 2007

Abstract

Small area estimation methods are typically used by government agencies for official statistics. In general, surveys conducted by governments are based on country level sample designs because officials are mainly interested in country level statistics. Thus small area estimation methods are very useful for the small areas or domains of official statistics. In this paper, we suggest four small area estimation methods: a Bayesian Poisson regressive model (BPRM), a Bayesian auto-Poisson model (BAPM), a conditional autoregressive (CAR) model and a Bayesian conditional autoregressive model (BCAR). The effciency of the four methods are compared using the bias checking method (Brown et al. [2]) and MSE. In this study, discrete, rare event and spatially correlated data from the survey of the disabled population in a specific country are used  for the analysis.

Keywords and phrases: Bayesian auto-Poisson model, Bayesian Poisson regression model, conditional auto regressive model, Bayesian conditional auto regressive model, Moran’s index.