Small area estimation models with time factor effects for repeated measurement data

Abstract

There has been an increasing demand for small area statistics based on sample survey in last few years. Generally, sample survey is designed for a specific area with large sample size. Since the sample size of a specific area is small, a direct estimation for sub population fails to provide enough precision. On the other hand, the per capita expenditure as a measure of prosperity and well-being is becoming an important issue in developing countries. In Indonesia, the available data related to this issue is usually measured repeatedly in quarterly using the national social-economic survey (Susenas). There are two problems to analyze Susenas data in district level. Firstly, the sample size in each quarter is relatively small. Secondly, the auxiliary data usually is available yearly only. To overcome this problem, a proper estimation technique was exercised using modeling systems. An extended of small area estimation (SAE) technique, based on both Fay-Herriot and Rao-Yu models in repeated measurement using Susenas data was discussed. Especially, SAE models with time factor effects motivated by Rao and Yu [7] were proposed. The performances of these models were evaluated by comparing the root mean square error (RMSE) and coefficient of variation (CV) of the estimators. The results showed that Rao-Yu with time factor effect models produced smaller RMSE which led to a significant reduction in a CV relative to other models.