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A simulation study: Using dual ancillary variable to estimate population mean under stratified random sampling.

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Summary

This study introduces an improved estimator for finite population mean using stratified random sampling. The new method enhances estimation precision by incorporating an ancillary variable and its rank, outperforming existing techniques.

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Accurate estimation of finite population parameters is crucial in statistical surveys.
  • Stratified random sampling is a common technique to improve precision.
  • Existing estimators may not fully leverage available ancillary information.

Purpose of the Study:

  • To propose an improved ratio-in-regression type estimator for the finite population mean.
  • To enhance estimation precision in stratified random sampling by utilizing ancillary variables and their ranks.
  • To provide a theoretical and numerical comparison with existing estimators.

Main Methods:

  • Development of a novel ratio-in-regression type estimator.
  • Derivation of bias and mean square error expressions up to the first order of approximation.
  • Empirical evaluation using two real data sets and a simulation study.

Main Results:

  • The proposed estimator demonstrates improved performance compared to existing methods.
  • The use of ancillary variables and their ranks significantly enhances estimation precision.
  • Theoretical derivations and numerical results confirm the superiority of the new estimator.

Conclusions:

  • The proposed estimator offers a more precise estimation of the finite population mean.
  • Effective utilization of ancillary information is key to improving survey estimates.
  • This work contributes a valuable tool for survey statisticians.