Optimized inferences of finite population mean using robust parameters in systematic sampling.

Area of Science:

• Statistics
• Survey Methodology

Background:

• Accurate mean estimation is crucial in survey sampling.
• Auxiliary information can improve estimation precision.
• Existing ratio and regression estimators have limitations.

Purpose of the Study:

• To propose a generalized estimator for mean estimation.
• To improve precision in systematic sampling using auxiliary information.
• To incorporate robust parameters for enhanced estimates.

Main Methods:

• Combining ratio and regression methods of estimation.
• Utilizing auxiliary variable parameters.
• Deriving bias and mean square error under large sample approximation.
• Systematic sampling technique.

Main Results:

• The proposed generalized estimator offers improved precision.
• Various existing estimators can be derived from the proposed one.
• Mathematical conditions for superior performance are identified.
• Empirical evaluation on four populations demonstrates efficiency.

Conclusions:

• The generalized estimator is efficient and useful for survey sampling.
• It outperforms traditional ratio, product, and regression estimators.
• The method provides a robust approach to mean estimation with auxiliary data.