Regression estimator under inverse sampling to estimate arsenic contamination

Abstract

The fate of arsenic introduced to the environment as a result of the natural and human activities is an important issue. Surveys of arsenic typically involve sampling from a large area. Measuring arsenic concentrations in samples is expensive, and any improvement in the survey design is welcome. One way to improve efficiency in sampling is to make use of auxiliary information. Surveys of environmental pollution can be classed as surveys of rare populations, where there is a large area with a small polluted subarea. The rare population has many zeroes, or low, values, and contaminated subareas have non-zero, or high, values. Regression estimators or ratio estimators are undefined for those samples containing only information from the non-rare (zero-value) subpopulation (i.e., the non-contaminated subpopulation) in simple random sampling. In this paper, we introduce the modified regression estimators and their associated variance estimators for sampling designs which are suitable for rare populations, such as general inverse sampling and inverse sampling with unequal selection probabilities. We conducted a simulation study on the real rare population arsenic contamination in Kurdistan. The simulation results showed that the modified regression estimators are more efficient than the previous estimators. Copyright © 2011 John Wiley & Sons, Ltd.