A Class of Population Mean Estimators in the Presence of Missing Data with Applications to Air Pollution in Chiang Mai, Thailand

The prevailing hazard of air pollution in Chiang Mai is constantly increasing in severity as a result of the burning of agricultural areas which can be harmful to human life. Knowing the pollution data in advance can assist the government in planning to mitigate the ongoing issue for Thai people. However, the pollution data set contains some missing data. Ignoring missing data may lead to bias in the estimation process. The imputation technique can be used to handle missing data before moving on to further analysis. A general class for population mean based on the imputation method when data are missing in the study variable is proposed under simple random sampling without replacement. The bias and mean square error of the proposed estimators are considered up to the first order of approximation. A general class of estimators are applied to air pollution data in northern Thailand to assess their performance. The results from the pollution data illustrate that the proposed estimators give the minimum mean square error for all levels of sampling fractions.