| Summary: | 博士 === 國立政治大學 === 統計學系 === 87 === Small area estimation is getting more important because of a growing demand for reliable small area statistics. In Taiwan, labor force series of local governments are likely to yield unacceptably large standard errors due to unduly small size of the sample in the areas. In this paper, we propose four methods to find more accurate estimates for given small areas.
First of all, we construct a composite estimator for the labor force series and evaluate it using relative efficiency. Secondly, we develop alternative estimates, mixed effects model and simultaneous auto-regression model, which borrow strength from neighboring small areas. We solve the important problem of small area estimation by creating a mixed effects model for cross-sectional and time series data, and overcome the lack of auxiliary data. Simultaneous auto-regression models are constructed to describe the spatio-temporal relationship between neighboring small areas. Finally, we use Bayes theory and characteristic of the survey design to develop an empirical Bayes estimator.
Besides, some discussion and conclusion of the previous methods are given to compare with the current survey estimates. To sum up, mixed effects model and simultaneous auto-regression model can reduce the variation of the current survey estimates, but the computations are relatively complex. The empirical Bayes estimator has three characteristics. First, the assumption is based on the slowly changing of labor force series. Secondly, it achieves the expected goal of variance reduction. Finally, the computation procedure is very simple. Therefore, empirical Bayes estimator is a potential method for small area estimation.
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