Improved confidence intervals for a small area mean under the Fay-Herriot model
Shiferaw, Yegnanew Alem
There is a growing demand for small area estimates for policy and decision making, local planning and fund distribution. Surveys are generally designed to give representative estimates at national or regional level, but estimates of variables of interest are often also needed at the small area levels. These cannot be reliably obtained from the survey data as the sample sizes at these levels are too small. This problem is addressed by using small area estimation techniques. The main aim of this thesis is to develop confidence intervals (CIs) which are accurate to terms O(m–3/2 ) under the FH model using the Taylor series expansion. Rao (2003a), among others, notes that there is a situation in mixed model estimation that the estimates of the variance component of the random effect, A, can take negative values. In this case, Prasad and Rao (1990) consider ˆA = 0. Under this situation, the contribution of the mean squared error (MSE) estimate, assuming all parameters are known, becomes zero. As a solution, Rao (2003a) among others proposed a weighted estimator with fixed weights (i.e., wi = 12 ). In addition, if the MSE estimate is negative, we cannot construct CIs based on the empirical best linear unbiased predictor (EBLUP) estimates. Datta, Kubokawa, Molina and Rao (2011) derived the MSE estimator for the weighted estimator with fixed weights which is always positive. We use their MSE estimator to derive CIs based on this estimator to overcome the above difficulties. The other criticism of the MSE estimator is that it is not area-specific since it does not involve the direct estimator in its expression. Following Rao (2001), we propose area specific MSE estimators and use them to construct CIs. The performance of the proposed CIs are investigated via simulation studies and compared with the Cox (1975) and Prasad and Rao (1990) methods. Our simulation results show that the proposed CIs have higher coverage probabilities. These methods are applied to standard poverty and percentage of food expenditure measures estimated from the 2010/11 Household Consumption Expenditure survey and the 2007 census data sets. Keywords: Small area estimation, Weighted estimator with fixed weights, EBLUP, FH model, MSE, CI, Poverty, percentage of food expenditure
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the Degree of Doctor of Philosophy. Johannesburg, August 2016.
Shiferaw, Yegnanew Alem (2016) Improved confidence intervals for a small area mean under the Fay-Herriot model, University of Witwatersrand, Johannesburg, <http://wiredspace.wits.ac.za/handle/10539/21689>