<p>A small area in survey sampling is a subpopulation or geographic region within a larger population where reliable statistical estimates are difficult due to limited sample sizes. Accurate small area estimation is crucial, particularly in overlapping population frames. This study extends a work of Hartley’s to propose a direct estimator for small areas under dual frame sampling, incorporating known domain sizes. which integrates sample means from overlapping frames, weighted by sample size proportions, to enhance precision. Variance estimation is complex due to overlapping frames with unknown frame membership, addressed using a stratified naïve Bootstrap method. A simulation of 4000 units across five small areas under different population distributions compares the proposed estimator with Horvitz-Thompson and Hartley estimators. Results show superior precision, reduced bias, and lower Percent Relative Bias (%RB) and Percent Relative Root Mean Square Error (%RRMSE). The bootstrap method further refines variance estimation, ensuring lower %RB and greater relative stability (RS). Further, an application of the proposed technique was demonstrated using real survey data and the results indicate that the dual-frame estimation approach improves population coverage and enhances the reliability of small area estimates, even when the individual sampling frames are incomplete.</p>

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Estimation of Small Area Parameter Under Dual Frame Surveys with Known Domain Sizes

  • Veershetty,
  • Tauqueer Ahmad,
  • Ankur Biswas,
  • Prachi Misra Sahoo,
  • Moumita Baishya

摘要

A small area in survey sampling is a subpopulation or geographic region within a larger population where reliable statistical estimates are difficult due to limited sample sizes. Accurate small area estimation is crucial, particularly in overlapping population frames. This study extends a work of Hartley’s to propose a direct estimator for small areas under dual frame sampling, incorporating known domain sizes. which integrates sample means from overlapping frames, weighted by sample size proportions, to enhance precision. Variance estimation is complex due to overlapping frames with unknown frame membership, addressed using a stratified naïve Bootstrap method. A simulation of 4000 units across five small areas under different population distributions compares the proposed estimator with Horvitz-Thompson and Hartley estimators. Results show superior precision, reduced bias, and lower Percent Relative Bias (%RB) and Percent Relative Root Mean Square Error (%RRMSE). The bootstrap method further refines variance estimation, ensuring lower %RB and greater relative stability (RS). Further, an application of the proposed technique was demonstrated using real survey data and the results indicate that the dual-frame estimation approach improves population coverage and enhances the reliability of small area estimates, even when the individual sampling frames are incomplete.