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

ýSmall area estimates have received much attention from both private and public sectors due to the growing demand for effective planning of health servicesý, ýapportioning of government funds and policy and decision makingý. ýSurveys are generally designed to give representative estimates at national or district levelý, ýbut estimates of variables of interest are often also needed at lower levelsý. ýThese cannot be reliably obtained from the survey data as the sample sizes at these levels are too smallý. ýCensus data is often availableý, ýbut only gives limited information with respect to the variables of interestý. ýThis problem is addressed by using small area estimation techniquesý, ýwhich combine the estimates from the survey and census data setsý. ýThe main purpose of this paper is obtaining confidence intervals based on the empirical best linear unbiased predictor (EBLUP) estimatesý. ýOne 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 expressioný. ýHoweverý, ýmost of the confidence intervals in the literature are constructed based on those MSEsý. ýIn this paperý, ýwe propose area specific confidence intervals for small area parameters under the Fay-Herriot model using area specific MSEsý. ýWe extend these confidence intervals to the difference between two small area meansý. ýThe effectiveness of the proposed methods are also investigated via simulation studies and compared with the Cox (1975) and Prasad and Rao (1990) methodsý. ýOur simulation results show that the proposed methods have higher coverage probabilitiesý. ýThose 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 setsý.