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An efficient logarithmic estimator in stratified random sampling using single auxiliary variable.

Fazal Shakoor1, Muhammad Asif2, Muhammad Atif3

  • 1Department of Statistics, University of Peshawar, Peshawar, Pakistan.

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|February 26, 2026
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Summary
This summary is machine-generated.

A new logarithmic-type estimator improves population mean estimation in stratified random sampling using auxiliary variables. This novel approach enhances survey accuracy and efficiency, outperforming existing methods in simulations and real-world data analysis.

Keywords:
AuxiliaryBiasEfficiencyLogarithmic estimatorMSEPRERatio estimatorStratified random sampling

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Accurate estimation of population means is crucial in statistical surveys.
  • Stratified random sampling is a common technique, often enhanced by auxiliary information.
  • Existing estimators may not fully leverage auxiliary variables for improved precision.

Purpose of the Study:

  • To propose a novel logarithmic-type estimator for population mean estimation.
  • To enhance the utilization of a single auxiliary variable in stratified random sampling.
  • To improve estimation accuracy and efficiency compared to existing methods.

Main Methods:

  • Development of a logarithmic-type estimator.
  • Derivation of analytical expressions for bias and precision.
  • Empirical evaluation using real-life datasets and simulation studies.
  • Comparison with existing estimators under varying sample sizes (n=50, 100, 150).

Main Results:

  • The proposed estimator demonstrates higher percentage relative efficiency.
  • Superior precision was consistently observed across real and simulated datasets.
  • Theoretical conditions for the proposed estimator dominating existing ones were established.
  • Significant gains in survey accuracy were noted, especially with strong variable association.

Conclusions:

  • The novel logarithmic-type estimator offers substantial improvements in survey accuracy.
  • Effective exploitation of auxiliary information leads to enhanced estimation precision.
  • The proposed method is a valuable advancement for survey statisticians using auxiliary variables.