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

In this context, supposing a sampling survey framework and a model-basedapproach, the attention has been focused on the main features of the optimal predictionstrategy of a given population mean, which implies estimation of some model parametersand functions, normally unknown. In particular, a wrong specification of the single unitmodel variances may lead to a serious loss of efficiency of estimates. For this reason, wehave proposed some techniques for the estimation of model variances, which instead ofbeing put equal to given a priori functions, can be estimated through historical dataconcerning past survey occasions. This approach is pragmatic and realistic, since quitealways a time series of past observations is available, especially in a longitudinal surveycontext. Moreover, a simple post-stratification method has been proposed, in order to betterdefine the models which can explain observed data. Finally, a comparative non parametricdonor imputation procedure has been considered, which may be used separately or coupledwith model assisted estimation. Usefulness of the techniques proposed has been testedthrough an empirical attempt, concerning the quarterly wholesale trade survey carried out byISTAT (Italian National Statistical Institute) in the period 2005-2010. In this framework, theproblem consists in minimizing magnitude of revisions, given by the differences betweenpreliminary 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 variancesestimation through historical data leads to efficiency gains (lower average revisions) whichcannot be neglected, and that model based prediction is normally more efficient thangeneralized regression estimation (which takes into account the sampling design randomnessas well). Moreover, in many cases the mixed procedure (joint use of estimations of modelunit variances through historical data, post-stratification and donor imputation) can improveprecision of preliminary estimates even more.