Authors:Yegnanew Shiferaw (University of Johannesburg, South Africa)Jacqueline S. Galpin (University of the Witwatersrand, South Africa)
There is a growing demand on small area estimates for policy and decision making, local planning and fund distribution. The best known small area estimation model, which is called the Fay-Herriot (FH) model is considered here. There is a situation in mixed model estimation that the estimates of the variance component of the random effect can take negative values. In practice the estimate of the variance of the random effect is often set to zero. Under this situation, the contribution of the mean squared error (MSE) estimate, assuming all parameters are known, becomes zero. In addition, if the MSE estimate is negative, we cannot construct confidence intervals (CIs) based on the empirical best linear unbiased predictor (EBLUP). As a solution, we develop a second order corrected CIs for the small area means based on the weighted estimator with fixed weights under the FH model. Furthermore, CIs for two or more population means is still an area to which very little attention has been paid. In this paper we proposed CIs for the difference of two small area means based on the weighted estimator with fixed weights which is second order correct under unequal sampling variances. The performance of the proposed CIs are investigated via simulation studies and compared with the conventional CIs. Our simulation results show that the proposed CIs have higher coverage probabilities. These methods are applied to percentage of food expenditure measures using the 2010/11 Household Consumption Expenditure survey and the 2007 census data sets.