Benchmark estimators for a small area mean under a one-fold nested regression model



Mike Hidiroglou (Statistics Canada) (Speaker)
Marius Stefan (Polytechnic University of Bucharest)

The authors develop a number of small area estimation procedures using a unit level linear regression model and survey weights: these weights incorporate the auxiliary information at the sample level. In particular, they propose three ways to ensure that the You-Rao (2002), Prasad-Rao (1999) and EBLUP small area estimators add up to estimates over the whole sample or subsets of it. The overall estimates may have been obtained by the GREG estimator or calibration. The first procedure consists in You-Rao (2002) type predictors that incorporate the GREG or calibrated weights so as to obtain the required benchmarking. The second and third procedures use the idea of augmented models using suitable additional explanatory variables. The second procedure uses the idea developed by Qu, Fuller and Wang (2008) by augmenting the aggregated area level model. It results in Prasad-Rao (1999) type predictors that achieve the self-calibrated property. The third method augments the unit level model by a variable equal to the GREG weights. The resulting EBLUP type predictors verify the benchmark relation. The estimated mean squared estimators of the resulting estimators can be obtained directly by suitably modifying the mse estimators of the corresponding unit level models that do not satisfy the benchmarking. The properties of the estimators are evaluated via a simulation.

Prasad, N.G.N. and Rao, J.N.K. (1999). On robust small area estimation using a simple random effects model. Survey Methodology, 25, 67-72. Wang, J., Fuller, W.A. and Qu, Y. (2008). Small area estimation under a restriction, Survey Methodology, 1, 29-36. You, Y. and Rao, J.N.K. (2002) A pseudo-empirical best linear unbiased prediction approach to small area estimation using survey weights. The Canadian Journal of Statistics, 30, 3, 431-439
Keywords: EBLUP, Prasad-Rao. You-Rao, small area, benchmarking

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