Area specific confidence intervals for a small area mean under the Fay-Herriot model

‎Small area estimates have received much attention from both private and public sectors due to the growing demand for effective planning of health services‎, ‎apportioning of government funds and policy and decision making‎. ‎Surveys are generally designed to give representative estimates at national or district level‎, ‎but estimates of variables of interest are often also needed at lower levels‎. ‎These cannot be reliably obtained from the survey data as the sample sizes at these levels are too small‎. ‎Census data is often available‎, ‎but only gives limited information with respect to the variables of interest‎. ‎This problem is addressed by using small area estimation techniques‎, ‎which combine the estimates from the survey and  census data sets‎. ‎The main purpose of this paper is obtaining confidence intervals based on the empirical best linear unbiased predictor (EBLUP) estimates‎. ‎One of the criticism of the mean squared error (MSE) estimators  is that it is not area-specific since it does not involve the direct estimator in its expression‎. ‎However‎, ‎most of the confidence intervals in the literature are constructed based on those MSEs‎. ‎In this paper‎, ‎we propose area specific confidence intervals for small area parameters under the Fay-Herriot model using area specific MSEs‎. ‎We extend these confidence intervals to the difference between two small area means‎. ‎The effectiveness of the proposed methods are also investigated via simulation studies and compared with the Cox (1975) and Prasad and Rao (1990) methods‎. ‎Our simulation results show that the proposed methods have higher coverage probabilities‎. ‎Those methods are applied to the percentage of food expenditure measures in Ethiopia using the 2010/11 Household Consumption Expenditure (HCE) survey and the 2007 census data sets‎.