Enhanced Variance Estimation Techniques for Addressing Non-Response and Measurement Error Situations

Abstract

The use of relevant information from auxiliary variables at the estimation stage and design stage to obtain reliable and efficient  estimates is a common practice in a sample survey. Several Estimators of population variance have been suggested. However, these  estimators do not consider the situation of non-response due to non-availability of respondents, refusal to respond, presence of hard- core respondents or due to non-understanding of the question thereby, reducing the efficiency of the estimators and the parameters of  the auxiliary variable X̄ , S²_x used are sensitive to outliers or extreme values which can either lead to underestimation or overestimation.  To address the aforementioned observations, classes of variance estimators under the simultaneous influence of non-response and measurement errors using outlier-free parameters as well as calibration approaches were proposed. The properties (Bias and MSE) of  the modified estimators were derived up to the first order of approximation using the Taylor series approach. The efficiency conditions of  the proposed estimators over the existing estimators considered in the study were established. The empirical studies were conducted  using simulation and the results revealed that the proposed class of estimators have minimum MSEs and higher PREs among all the  competing estimators. These imply that the proposed estimators are more efficient and can produce a better estimate of the population  mean compared to other existing estimators considered in the study.