Variance of the direct estimators Sample Clauses

Variance of the direct estimators. In the production of small area estimates using a procedure such as combined estimation, a major requirement is that of evaluating the reliability of the direct estimates. To achieve this goal we basically need to estimate their variances and, eventually, to apply small area multivariate models (Xxx 2003). We need also to estimate the covariances between estimators of different rates obtained for the same domain. Evaluating the variances and covariances of the direct estimators is not an easy task for the EU SILC survey, since: i) the considered poverty rates are non­linear functions of data; ii) the underlying design is complex; iii) the weights used in their computation incorporate, as it has been previously described, two stages of calibration corrections. Other works in this field (Xxxxx and Xxxxx, 2005; Xxxxx and Xxxxx, 2006) suggest a solution based on re­sampling algorithms and in particular on the bootstrap estimation strategy. For stratified multistage designs one solution is that proposed by XxXxxxxx and Xxxxxxx (1985). This bootstrap procedure is an asymptotically valid method in assessing the variability of direct estimators. Specifically, every bootstrap sample is obtained drawing with­replacement a random sample of n­1 PSU’s out the n at disposal in the stratum. After every re­sampling, the original weights are properly rescaled and the bootstrap variance estimate of the corresponding indicator is obtained by the usual Monte Carlo approximation based on the independent bootstrap replicates. For every LAU1 or LAU2 area the variance of the direct estimator is calculated in the following way ψ = V (θˆ )= 1 ∑N (θˆ*b −θˆ* ) i i