Using composite estimators to improve both domain and total area estimation
In this article we propose using small area estimators to improve the estimates of both the small and large area parameters. When the objective is to estimate parameters at both levels accurately, optimality is achieved by a mixed sample design of fixed and proportional allocations. In the mixed sample design, once a sample size has been determined, one fraction of it is distributed proportionally among the different small areas while the rest is evenly distributed among them. We use Monte Carlo simulations to assess the performance of the direct estimator and two composite covariant-free small area estimators, for different sample sizes and different sample distributions. Performance is measured in terms of Mean Squared Errors (MSE) of both small and large area parameters. It is found that the adoption of small area composite estimators open the possibility of 1) reducing sample size when precision is given, or 2) improving precision for a given sample size.
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- Farrell, Patrick J & MacGibbon, Brenda & Tomberlin, Thomas J, 1997. "Empirical Bayes Small-Area Estimation Using Logistic Regression Models and Summary Statistics," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 101-108, January.
- Àlex Costa & Albert Satorra & Eva Ventura, 2003. "An empirical evaluation of small area estimators," Economics Working Papers 674, Department of Economics and Business, Universitat Pompeu Fabra, revised Jun 2003.
- Alex Costa & Albert Satorra & Eva Ventura, 2003. "An Empirical Evaluation of Five Small Area Estimators," General Economics and Teaching 0312003, EconWPA.
- Isaki, Cary T, 1990. "Small-Area Estimation of Economic Statistics," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(4), pages 435-441, October.
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