Estimation of Design Mean Square Error in Small Area Estimation


Keynote Session – Danny Pfeffermann

Author: Danny Pfeffermann (Central Bureau of Statistics in Israel, University of Southampton, Hebrew University of Jerusalem)

Traditional MSE estimators in small area estimation account for all sources of variation, including in particular the distribution of the target population parameters (the random effects) under the assumed model. Often, however, users of the small area predictors prefer the MSE estimators to condition on the true unknown population values, such that they only account for the variance component induced by the random sample selection. This is in line with traditional variance estimators published by National Statistical Institutes producing official statistics, commonly known as design-based estimators.


While many researchers agree that the Design MSEs may be of interest, concern is raised that it is practically impossible to estimate them sufficiently accurately, with only a small sample available for a given area.  MSE estimators are required for each area separately, irrespective of how they are computed.


In this presentation we shall describe a method of estimating the design MSE, which attempts to model the MSE as a function of statistics computed from the sample data. The key to the success of the method is the identification of a good functional relationship. We illustrate the performance of the method in estimating the design MSE of the Fay-Herriot predictors. While the results are yet not fully satisfactory, the method does perform much better than the naïve, approximately design unbiased estimator. We hope to also compare our estimator to other design NSE estimators proposed in the literature.