A note on a difference-type estimator for population mean under two-phase sampling design

Area of Science:

• Statistics
• Survey Methodology

Background:

• Accurate estimation of population parameters is crucial in statistical surveys.
• Two-phase sampling designs offer efficiency gains by utilizing auxiliary information.
• Existing estimators may not fully leverage available auxiliary variables.

Purpose of the Study:

• To propose a novel difference-type estimator for the population mean.
• To evaluate the performance of the proposed estimator under a two-phase sampling scheme.
• To compare the efficiency of the new estimator against existing methods.

Main Methods:

• Development of a difference-type estimator incorporating two auxiliary variables.
• Derivation of the estimator's properties and mean square error (MSE) up to the first order of approximation.
• Efficiency comparisons with existing estimators under the two-phase sampling framework.

Main Results:

• The proposed estimator's properties and MSE were theoretically derived.
• Conditions for the proposed estimator's superior efficiency were identified.
• Empirical evidence suggests the proposed estimator outperforms existing ones in a specific case.

Conclusions:

• The proposed difference-type estimator demonstrates potential for enhanced efficiency in two-phase sampling.
• Further research is recommended to validate its superiority across diverse populations.
• The findings contribute to the advancement of survey estimation techniques.