Weighting in survey sampling

In sampling surveys weighting is applied to data to increase the quality of estimates. Weighting in data is realized as a multi stage process to reduce the differences of the selection probabilities of sampling units, to avoid nonresponse, noncoverage bias and so as to make the sampling distribution match with population distribution. In this study the Horvitz-Thompson [1952] and Hájek [1971] estimators of the population parameters are examined in the probability sampling methods of simple random sampling, stratified random sampling and cluster sampling and the estimators structures given at weighting stages. The weighting methods of weighting class adjustment, poststratification, raking, calibration estimator and generalized regression (GREG) estimators are illustrated. Hájek [1971] estimator definitions of the weighting methods are presented. The staged calibration estimator is suggested. Demographic and Health Survey/Turkey 2003 data are taken for application purposes. For the survey data the precision of the parameter estimates are investigated with respect to the sampling, nonresponse, calibration weighting, stage calibration and Ayhan (2003) combined ratio estimator.