A new estimator for population total in the presence of missing data under unequal probability sampling without replacement: A case study on fine particulate matter in Northern Thailand

Abstract

The issue of fine particulate matter in Thailand, especially in Northern Thailand, is an urgent problem that needs to be solved because of potential harm to human health. Prior estimates of fine particulate matter help planning how to reduce it. The daily fine particulate matter data reports usually contain some missing values. An improved ratio estimator has been suggested for population total under unequal probability sampling without replacement. The improved estimator is studied under a reverse framework when the nonresponse mechanism is not uniform, called missing at random nonresponse, which is more convenient to apply in practice. The variance and its associated estimator are investigated in theory. Simulation studies are used to assess the suggested estimator’s performance. The new estimator is also applied to estimate fine particulate matter in Northern Thailand. The results show that the suggested estimator under the missing at random nonresponse mechanism performs well, as opposed to the existing estimator under missing completely at random assumption. The estimated fine particulate matter levels in Northern Thailand from the proposed estimator give a lesser variance than the existing one.

Keywords

• fine particulate matter
• ratio estimator
• nonresponse mechanism
• population total
• missing at random