A simulation study: Improved ratio-in-regression type variance estimator based on dual use of auxiliary variable...

Area of Science:

• Statistics
• Survey Methodology

Background:

• Accurate estimation of finite population variance is crucial in statistical surveys.
• Existing estimators may not fully leverage available auxiliary information for improved precision.

Purpose of the Study:

• To propose an improved finite population variance estimator.
• To enhance estimation accuracy by incorporating dual auxiliary information within a simple random sampling framework.

Main Methods:

• Developed a novel variance estimator using dual auxiliary variables.
• Derived mathematical expressions for proposed and existing estimators to the first order of approximation.
• Validated performance using two real data sets and a comprehensive simulation study.

Main Results:

• The proposed estimator achieved the minimum mean square error.
• Demonstrated higher percentage relative efficiency compared to all existing estimators.
• Simulation results confirmed the robustness and generalizability of the new estimator.

Conclusions:

• The proposed finite population variance estimator offers superior performance.
• Utilizing dual auxiliary information significantly improves estimation accuracy in simple random sampling.
• The new estimator is recommended for practical applications requiring precise variance estimation.