Optimality of classical difference estimators of finite population variance under random non-response with comparative study

In this study, we address the challenge of calculating the finite population variance when faced with random non-response. Such issues are commonly encountered in various fields like medical sciences, environmental sciences and business studies when dealing with data. Using the ranking of an auxiliary variable across three different methodologies of random non-response, we developed several novel difference-type estimators of population variance along with their optimal models. The strategies are shaped by using the varying levels of information available regarding the auxiliary variable. We have studied the properties of the proposed estimators under large sample approximations and determined their optimum situations in each strategy. The introduced estimators can be viewed as an advancement of traditional difference estimators. Within the associated methodologies, we conducted a comparative analysis based on some real datasets as well as simulated datasets, whereby the proposed estimators showed reduced variances when assessed in terms of the enhanced percentage relative efficiencies (PRE) compared to some standard ratio and difference-type estimators relevant to the respective methodologies.