Estimation of Model Variance Functions in Survey Sampling using Historical Micro-data

Abstract

In this context, supposing a sampling survey framework and a model-based approach, the attention has been focused on the main features of the optimal prediction strategy of a given population mean, which implies estimation of some model parameters and functions, normally unknown. In particular, a wrong specification of the single unit model variances may lead to a serious loss of efficiency of estimates. For this reason, we have proposed some techniques for the estimation of model variances, which instead of being put equal to given a priori functions, can be estimated through historical data concerning past survey occasions. This approach is pragmatic and realistic, since quite always a time series of past observations is available, especially in a longitudinal survey context. Moreover, a simple post-stratification method has been proposed, in order to better define the models which can explain observed data. Finally, a comparative non parametric donor imputation procedure has been considered, which may be used separately or coupled with model assisted estimation. Usefulness of the techniques proposed has been tested through an empirical attempt, concerning the quarterly wholesale trade survey carried out by ISTAT (Italian National Statistical Institute) in the period 2005-2010. In this framework, the problem consists in minimizing magnitude of revisions, given by the differences between preliminary estimates (based on the sub-sample of quick respondents) and final estimates (which take into account late respondents as well). Main results show that model variances estimation through historical data leads to efficiency gains (lower average revisions) which cannot be neglected, and that model based prediction is normally more efficient than generalized regression estimation (which takes into account the sampling design randomness as well). Moreover, in many cases the mixed procedure (joint use of estimations of model unit variances through historical data, post-stratification and donor imputation) can improve precision of preliminary estimates even more. Keywords: Donor; Longitudinal Survey; Model; Non Response; Post-Stratification; Revision; Variance. 2010 Mathematics Subject Classification: 62D05