Introduction into Sampling Theory, Applying Partial Order Concepts

Abstract

In sampling theory, we are looking for efficient sampling designs to estimate the population parameters. Efficiency is mostly defined based on high precision and low cost. Such sampling designs are more achievable when auxiliary variables are available. Selecting many sampling units and rank them based on auxiliary variables before selecting the final sample, leads to a post-stratified population that provides a proper situation to select a good sample to estimate the population parameters more precisely but more costly relative to simple random sampling. Two challenges are in the way of using such designs; first, reducing costs of the designs, and second, ranking the units when there is more than one variable of interest for each unit. Here, in the way of overcoming these challenges we make a connection between sampling theory and partial order set theory. Based on some simulations we will show that applying partial order set theory in sampling designs, leads to a new more efficient design that increases the precision of estimating all the parameters simultaneously in the case of multivariate analysis.