Modification of Logarithmic-Type Estimators of Population Variance in Two-Phase-Successive Sampling with Random Non-Response and Measurement Errors
Musa Salihu
Abubakar Danbaba
Ahmed Audu
Abdulkarim Bello
Abstract
The estimation of population variance is a critical undertaking in survey sampling, with significant implications across fields such as agriculture, economics, and public health. However, the precision of such estimates is often
compromised by the dual challenges of non-response and measurement errors, particularly in successive sampling designs. Furthermore, many existing efficient estimators rely on the unrealistic and costly assumption of known population parameters for auxiliary variables. This study therefore proposes modified variance estimators designed to overcome these limitations. The research adopted a two-phase sampling approach within a successive sampling
framework to develop logarithmic-type estimators that do not require known population parameters for the auxiliary variables. The biases and Mean Square Errors (MSEs) of the proposed estimators were derived theoretically to firstorder approximation. A comprehensive simulation study was conducted to evaluate their performance using Absolute Relative Bias (ARB), MSE, and Percentage Relative Efficiency (PRE) as performance metrics, comparing them
against a conventional estimator. The results demonstrate that the proposed estimators, particularly those utilizing estimates from the large first-phase sample, are highly efficient. PRE values consistently exceeded 200% in many
scenarios, indicating a dramatic improvement in precision over the conventional method, while maintaining low bias. The study concludes that the modified estimators provide a viable, cost-effective, and accessible framework for
estimating population variance with enhanced precision in the presence of nonresponse and measurement errors, thereby offering a significant contribution to survey sampling theory and practice.
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