New estimators for estimating population total: an application to water demand in Thailand under unequal probability sampling without replacement for missing data

Abstract

Water shortage could play an imperative role in the future due to an influx of water demand when compared to water supplies. Inadequate water could damage human life and other aspects related to living. This serious issue can be prevented by estimating the demand for water to bridge the small gap between demand and supplies for water. Some water consumption data recorded daily may be missing and could affect the estimated value of water demand. In this article, new ratio estimators for estimating population total are proposed under unequal probability sampling without replacement when data are missing. Two situations are considered: known or unknown mean of an auxiliary variable and missing data are missing at random for both study and auxiliary variables. The variance and associated estimators of the proposed estimators are investigated under a reverse framework. The proposed estimators are applied to data from simulation studies and empirical data on water demand in Thailand which contain some missing values, to assess the efficacies of the estimators.

Keywords

• Water demand
• Population total
• Unequal probability sampling without replacement
• Taylor linearization approach
• Nonlinear estimator
• Logistic regression