On bootstrap based variance estimation under fine stratification

The primary focus of all sample surveys is on providing point estimates for the parameters of primary interest, and also estimating the variance associated with those point estimates to quantify the uncertainty. Larger samples and important measurement tools can help to reduce the point estimates' uncertainty. Numerous effective stratification criteria may be used in survey to reduce variance within stratum. In fine stratification design, the population is divided into numerous small strata, each containing a relatively small number of sampling units as one or two. This is done to ensure that certain characteristics or subgroups of the population are well-represented in the sample. But with many strata, the sample size within each stratum can become small, potentially resulting in higher errors and less stable estimates. The variance estimation process becomes difficult when we only have one unit per stratum. In that case, the collapsed stratum technique is the classical methods for estimating variance. This method, however, is biased and results in an overestimation of the variance. This paper proposes a bootstrap-based variance estimator for the total population under fine stratification, which overcomes the drawbacks of the previously explored estimation approach. Also, the estimator's properties were investigated. A simulation study and practical application on survey of mental health organizations data were done to investigate properties of the proposed estimators. The results show that the proposed estimator performs well.