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An optimal estimation approach in non-response under simple random sampling utilizing dual auxiliary variable for

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Summary

This study introduces new exponential estimators for cumulative distribution functions (CDF) using dual auxiliary variables to improve survey sampling precision, especially with non-response. The proposed methods demonstrate superior efficiency and reduced mean squared error in various non-response scenarios.

Keywords:
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Area of Science:

  • Statistics
  • Survey Methodology
  • Sampling Theory

Background:

  • Precise population parameter estimation in survey sampling necessitates incorporating auxiliary data.
  • Non-response in surveys can significantly reduce the efficiency and precision of estimators.
  • Utilizing auxiliary information, such as CDF, mean, and ranks, is crucial for enhancing estimators.

Purpose of the Study:

  • To improve the efficiency of population parameter estimators in the presence of non-response.
  • To develop enhanced cumulative distribution function (CDF) estimators using dual auxiliary variables.
  • To investigate the performance of new exponential estimators under various non-response situations.

Main Methods:

  • Development of two families of exponential estimators utilizing dual auxiliary variables (CDF, mean, ranks).
  • Application of first-order approximation to determine bias and mean squared error (MSE) for new and existing estimators.
  • Evaluation of estimator performance across three non-response situations: non-response in both study and auxiliary variables, only study variable, or only auxiliary variable.

Main Results:

  • The proposed exponential estimators demonstrate increased precision and efficiency in estimating the CDF under non-response.
  • Significant improvements in Percentage Relative Efficiency (PRE) were observed, with values reaching up to 223.06% for k=2 and 223.06% for k=3.
  • The new estimators consistently yield lower Mean Squared Error (MSE) compared to existing methods across all simulated non-response scenarios.

Conclusions:

  • The suggested families of exponential estimators are effective and suitable for estimating distribution functions with dual auxiliary information, even with non-response.
  • The proposed estimators offer a statistically sound approach to mitigate the impact of non-response in survey sampling.
  • The study confirms the superiority of the new estimators in terms of efficiency and accuracy for CDF estimation.