On the Estimation of Mean Square Error of Small Area Predictors

نویسندگان

  • Prasad
  • J. N. K. Rao
چکیده

Small area estimation has received considerable attention in recent years due to growing demand for reliable small area statistics• The usual survey estimates, based only on the data from a given small area (domain), are likely to be unreliable due to smallness of sample size in the domain. Therefore, alternative estimators which "borrow strength" from other areas have been proposed in the literature to improve the efficiency. These estimators use models, either explicitly or implicitly, that "connect" the small areas through supplementary data (e.g., census and administrative data). Simple synthetic estimators, for example, are based on implicit modelling. In this paper, three small area models, due to Battese and Fuller (1982), Dempster et al. (1981) and Fay and Herriot (1979) respectively, are investigated. The best linear unbiased predictor (BLUP) under each model is obtained, using the general theory of Henderson (1975) for a mixed linear model. A weighted jackknife estimator of BLUP is also derived. Second order approximations to the mean square error (MSE) of estimated BLUP and the estimate of MSE are obtained, under normality. Robust estimates of the MSE approximation are also derived, using the weighted jackknife method. Finally, the results of a Monte Carlo study, on the efficiency of estimated BLUPs and the accuracy of the proposed approximations to MSE and its estimates, are reported•

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تاریخ انتشار 2002