Alternative adjustments where there are several levels of auxiliary information

Regression estimation and its generalization, calibration estimation, introduced by Deville and Särndal in 1993, serves to reduce a posteriori the variance of the estimators through the use of auxiliary information. In sample surveys, there is often useable supplementary information that is distributed according to a complex schema, especially where the sampling is realized in several phases. An adaptation of regression estimation was proposed along with its variants in the framework of two-phase sampling by Särndal and Swensson in 1987. This article seeks to examine alternative estimation strategies according to two alternative configurations for auxiliary information. It will do so by linking the two possible approaches to the problem: use of a regression model and calibration estimation.