The effect of model choice in estimation for domains, including small domains - ARCHIVED

In this paper, we examine the effects of model choice on different types of estimators for totals of domains (including small domains or small areas) for a sampled finite population. The paper asks how different estimator types compare for a common underlying model statement. We argue that estimator type - synthetic, generalized regression (GREG), composite, empirical best linear unbiased predicition (EBLUP), hierarchical Bayes, and so on - is one important aspect of domain estimation, and that the choice of the model, including its parameters and effects, is a second aspect, conceptually different from the first. Earlier work has not always made this distinction clear. For a given estimator type, one can derive different estimators, depending on the choice of model. In recent literature, a number of estimator types have been proposed, but there is relatively little impartial comparisons made among them. In this paper, we discuss three types: synthetic, GREG, and, to a limited extent, composite. We show that model improvement - the transition from a weaker to a stronger model - has very different effects on the different estimator types. We also show that the difference in accuracy between the different estimator types depends on the choice of model. For a well-specified model, the difference in accuracy between synthetic and GREG is negligible, but it can be substantial if the model is mis-specified. The synthetic type then tends to be highly inaccurate. We rely partly on theoretical results (for simple random sampling only) and partly on empirical results. The empirical results are based on simulations with repeated samples drawn from two finite populations, one artificially constructed, the other constructed from the real data of the Finnish Labour Force Survey.