Weights Proportional to Size (WPS)-Multi Systematic Sampling Design

Researchers are always in pursuit of developing estimators with increased precision by incorporating the information of suitable auxiliary (size) variables either in the selection or in the estimator. For single dimensional population, in probability proportional to size sampling schemes, size information of auxiliary variable is used in the selection as well as in the estimation stage in pursuit of developing estimators of variable of interest with increased precision than even the gold standard simple random sampling. Motivated by this, an attempt has been made towards incorporating size information in the estimator in the selection as well as in the estimation stage in pursuit of developing estimator of population total of the study variable with increased precision for multi-dimensional population exhibiting linear trend.