Summary

For each survey, the standard process from collection to elaboration of survey data needs to be accomplished within a fixed period of time, i.e. the final estimates must be disseminated at the prefixed time t. In this context, direct estimators of the target parameters – based on the sampling units included in the Theoretical Sample (TS), selected by a probabilistic sampling design – are design unbiased and consistent; the sampling error depends on the variability of the phenomenon under study, on the planned sample size and on the effectiveness of the selection procedure. Direct estimators based on the Observed Sample (OS) – that is a subset of TS whose size depends on the total nonresponse rate – can be biased in function of the response process generating the OS.

We assign the term "preliminary" at the estimates computed using the statistical information available at time preceding the time t, on the basis of the OS denoted as Preliminary Sample (PS). The most straightforward practice in this situation is to apply the same estimation techniques utilised to produce the final estimates. Alternative estimation techniques should take under control the bias and the revision error, given by the difference between final and preliminary estimates. In order to test the quality of the preliminary estimator, the revision error should be evaluated for different survey occasions.

The main theoretical problem to be faced in a short-term preliminary estimation context concerns the possible self-selection of quick respondents, that can lead to biased estimates of the unknown population mean and variances. In the context of short-term business surveys – usually planned for estimating parameters such as indexes and their changes over time – one common method is based on the evaluation, for each design stratum, of the direct estimator of the index imputing the missing responses for the sampling units belonging to TS. Another type of procedure utilises the direct estimates of the design stratum indexes without imputation of the missing responses both in OS and in PS. These approaches can be based on imputation methods supposing no systematic differences between early and late respondents.

Preliminary estimation methods may be classified in function of the stage on which specific preliminary methods are applied. In fact, it is possible to identify methods that are acting:

• at the sampling design stage, by selecting a preliminary subsample of TS;
• at the estimation stage, in the following ways:
  1. by means of imputation techniques of missing data, that are applied to the non respondent units in TS but not in PS;
  2. by means of weighting adjustment, i.e. modifying the sampling weights assigned to the units in PS in order to take into account non respondents in TS;
  3. by applying direct and indirect estimators, using known population totals of auxiliary variables and/or time series of preliminary and final estimates of the variable of interest.

The techniques based on the selection of a preliminary sample and the methods requiring imputation and weighting adjustment are generally based on unit level models. These models use disaggregated auxiliary information coming from survey data at previous times and/or administrative register data. For the methods in the last class the relation between the variable of interest and the auxiliary variables is usually formalised through domain level models in which the auxiliary information is expressed in terms of domain known totals or estimates. In the last class fall an estimation technique developed by Rao et al. (1989) in which preliminary estimates are computed assuming AR(1) models for final estimates and the revision error. This is the main specific model-based procedure used for the computation of preliminary estimation and it is described in this module.

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