Improvement in variance estimation using transformed auxiliary variable under simple random sampling.

Area of Science:

• Statistics
• Survey Methodology
• Statistical Inference

Background:

• Accurate estimation of population variance is crucial in statistical analysis.
• Traditional ratio estimators rely on auxiliary variables but can be limited in efficiency.
• Transforming auxiliary variables offers a potential avenue for improving estimation precision.

Purpose of the Study:

• To develop a novel and efficient ratio estimator for population variance.
• To investigate the impact of transforming auxiliary variables on estimation efficiency.
• To theoretically and empirically validate the performance of the proposed estimators.

Main Methods:

• Formulation of a new ratio estimator using a transformed auxiliary variable.
• Derivation of the theoretical properties of the proposed estimators.
• Empirical and simulation studies to compare performance against existing estimators.

Main Results:

• The transformation of auxiliary variables leads to a substantial gain in efficiency.
• The newly developed estimators demonstrate superior performance compared to existing ones.
• Both theoretical derivations and simulation results confirm the enhanced efficiency.

Conclusions:

• The proposed ratio estimator using a transformed auxiliary variable is highly efficient.
• This novel approach provides a valuable improvement for estimating population variance.
• The findings are supported by rigorous theoretical analysis and practical simulations.