## International Statistical Review

- Internat. Statist. Rev.
- Volume 74, Number 2 (2006), 127-147.

### Survey Estimates by Calibration on Complex Auxiliary Information

Victor M. Estevao and Carl-Erik Särndal

#### Abstract

In the last decade, ** calibration estimation** has developed into an important field of research in survey sampling. Calibration is now an important methodological instrument in the production of statistics. Several national statistical agencies have developed software designed to compute calibrated weights based on auxiliary information available in population registers and other sources.

This paper reviews some recent progress and offers some new perspectives. Calibration estimation can be used to advantage in a range of different survey conditions. This paper examines several situations, including estimation for domains in one-phase sampling, estimation for two-phase sampling, and estimation for two-stage sampling with integrated weighting. Typical of those situations is ** complex auxiliary information**, a term that we use for information made up of several components. An example occurs when a two-stage sample survey has information both for units and for clusters of units, or when estimation for domains relies on information from different parts of the population.

Complex auxiliary information opens up more than one way of computing the final calibrated weights to be used in estimation. They may be computed in a single step or in two or more successive steps. Depending on the approach, the resulting estimates do differ to some degree. All significant parts of the total information should be reflected in the final weights. The effectiveness of the complex information is mirrored by the variance of the resulting calibration estimator. Its exact variance is not presentable in simple form. Close approximation is possible via the corresponding linearized statistic. We define and use ** automated linearization** as a shortcut in finding the linearized statistic. Its variance is easy to state, to interpret and to estimate. The variance components are expressed in terms of residuals, similar to those of standard regression theory. Visual inspection of the residuals reveals how the different components of the complex auxiliary information interact and work together toward reducing the variance.

#### Article information

**Source**

Internat. Statist. Rev., Volume 74, Number 2 (2006), 127-147.

**Dates**

First available in Project Euclid: 24 July 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.isr/1153748788

**Keywords**

Official statistics production administrative registers calibrated weights design-based inference automated linearization integrated weighting ecological fallacy domains of interest two-stage sampling two-phase sampling

#### Citation

Estevao, Victor M.; Särndal, Carl-Erik. Survey Estimates by Calibration on Complex Auxiliary Information. Internat. Statist. Rev. 74 (2006), no. 2, 127--147. https://projecteuclid.org/euclid.isr/1153748788