Sampling design variance estimation of small area estimators in the Spanish Labour Force Survey

Abstract

The main goal of this paper is to Investigate how to estimate sampling design variances of modelbased and model-assisted small area estimators in a complex survey sampling setup. For this purpose the Spanish Labour Force Survey is considered. Sample and aggregated data are taken from the Canary Islands in the second trimester of 2003 in order to obtain some small area estimators of ILO unemployment totals. Several problems arising from the application of standard small area estimation procedures to the survey are described. It is shown that standard variance estimators based on explicit formulas are not applicable in the strict sense, since the assumptions under which they are derived do not hold. In addition two resampling techniques, bootstrap and jackknife, are considered. These methods treat all the considered estimators in the same manner and therefore they can be used as performance measures to compare them. From the analysis of the obtained results, some ecommendations are given.