New Variance Estimators in the Presence of Nonresponse Under Unequal Probability Sampling, with Application to Fine Particulate Matter in Thailand

Fine particulate matter exacerbates the environmental problem of air pollution in Thailand and contributes to premature deaths. Monitoring of levels of fine particulate matter data is imperative, however, values are seldom complete. One of the most important issues for variance estimation of population total estimators using ratio and generalized regression estimators under unequal probability sampling without replacement is that it requires joint inclusion probability which can be difficult to find. In this paper we solve this problem by proposing new variance estimators for population total in the presence of nonresponse under unequal probability sampling without replacement under the uniform nonresponse mechanism. Two approaches are used to construct the new variance estimators; estimating the joint inclusion probability and free joint inclusion probability. Simulation studies and an application to fine particulate matter in the north of Thailand are considered in the study. The results show that the variance estimators from the latter method give a smaller relative root mean square error and relative bias than the variance estimator from the former one. Nevertheless, the proposed variance to others.