Modified variance estimators in the presence of simultaneous effects of measurement error and non-response using auxiliary variable

Abstract

The estimation of variance is crucial in recognizing the inherent diversity of natural items within any category. Survey sampling theories often assume that measurement error does not affect data collection observations, but in reality, deviations from true values lead to significant measurement errors, especially when respondents provide insufficient or no information—a situation known as nonresponse. This study investigates the simultaneous impact of measurement error and nonresponse on estimating finite population variance under simple random sampling (SRS) design, employing auxiliary variables. Proposed estimators for the study variable Y combine sample variance, ratio estimation, and exponential estimation based on various means. Through Taylor expansion, first-order mean square errors (MSEs) and approximate biases for the estimators are derived, and their efficiency is compared with existing methods. A numerical study is also conducted to confirm the efficacy of the proposed estimators.